Relevant bibliographies by topics / Bergman metrics

Academic literature on the topic 'Bergman metrics'

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Published: 6 September 2023
Last updated: 7 September 2023

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Journal articles on the topic "Bergman metrics"

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Herbort, Gregor. "The growth of the bergman kernel on pseudoconvex domains of homogeneous finite diagonal type." Nagoya Mathematical Journal 126 (June 1992): 1–24. http://dx.doi.org/10.1017/s0027763000003986.

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In this article we continue the investigations on invariant metrics on a certain class of weakly pseudoconvex domains which we began in [H 1]. While in that paper the differential metrics of Caratheodory and Kobayashi were estimated precisely, the present paper contains a sharp estimate of the singularity of the Bergman kernel and metric on domains belonging to that class.
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Potash, Eric. "Euclidean Embeddings and Riemannian Bergman Metrics." Journal of Geometric Analysis 26, no. 1 (October 26, 2015): 499–528. http://dx.doi.org/10.1007/s12220-015-9560-3.

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Feng, Renjie. "Bergman metrics and geodesics in the space of Kähler metrics on principally polarized abelian varieties." Journal of the Institute of Mathematics of Jussieu 11, no. 1 (June 21, 2011): 1–25. http://dx.doi.org/10.1017/s1474748011000119.

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AbstractIt is well known in Kähler geometry that the infinite-dimensional symmetric space $\mathcal{H}$ of smooth Kähler metrics in a fixed Kähler class on a polarized Kähler manifold is well approximated by finite-dimensional submanifolds $\mathcal{B}_k\subset\mathcal{H}$ of Bergman metrics of height k. Then it is natural to ask whether geodesics in $\mathcal{H}$ can be approximated by Bergman geodesics in $\mathcal{B}_k$. For any polarized Kähler manifold, the approximation is in the C0 topology. For some special varieties, one expects better convergence: Song and Zelditch proved the C2 convergence for the torus-invariant metrics over toric varieties. In this article, we show that some C∞ approximation exists as well as a complete asymptotic expansion for principally polarized abelian varieties.
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LOI, ANDREA. "BERGMAN AND BALANCED METRICS ON COMPLEX MANIFOLDS." International Journal of Geometric Methods in Modern Physics 02, no. 04 (August 2005): 553–61. http://dx.doi.org/10.1142/s0219887805000685.

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Ferrari, Frank, Semyon Klevtsov, and Steve Zelditch. "Simple matrix models for random Bergman metrics." Journal of Statistical Mechanics: Theory and Experiment 2012, no. 04 (April 25, 2012): P04012. http://dx.doi.org/10.1088/1742-5468/2012/04/p04012.

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Maitani, Fumio, and Hiroshi Yamaguchi. "Variation of Bergman metrics on Riemann surfaces." Mathematische Annalen 330, no. 3 (June 8, 2004): 477–89. http://dx.doi.org/10.1007/s00208-004-0556-8.

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BERMAN, ROBERT J. "BERGMAN KERNELS AND EQUILIBRIUM MEASURES FOR POLARIZED PSEUDO-CONCAVE DOMAINS." International Journal of Mathematics 21, no. 01 (January 2010): 77–115. http://dx.doi.org/10.1142/s0129167x10005933.

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Let X be a domain in a closed polarized complex manifold (Y,L), where L is a (semi-) positive line bundle over Y. Any given Hermitian metric on L induces by restriction to X a Hilbert space structure on the space of global holomorphic sections on Y with values in the k-th tensor power of L (also using a volume form ωn on X. In this paper the leading large k asymptotics for the corresponding Bergman kernels and metrics are obtained in the case when X is a pseudo-concave domain with smooth boundary (under a certain compatibility assumption). The asymptotics are expressed in terms of the curvature of L and the boundary of X. The convergence of the Bergman metrics is obtained in a more general setting where (X,ωn) is replaced by any measure satisfying a Bernstein–Markov property. As an application the (generalized) equilibrium measure of the polarized pseudo-concave domain X is computed explicitly. Applications to the zero and mass distribution of random holomorphic sections and the eigenvalue distribution of Toeplitz operators will be described elsewhere.
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Feng, Zhiming. "The first two coefficients of the Bergman function expansions for Cartan–Hartogs domains." International Journal of Mathematics 29, no. 06 (June 2018): 1850043. http://dx.doi.org/10.1142/s0129167x1850043x.

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Let [Formula: see text] be a globally defined real Kähler potential on a domain [Formula: see text], and [Formula: see text] be a Kähler metric on the Hartogs domain [Formula: see text] associated with the Kähler potential [Formula: see text]. First, we obtain explicit formulas of the coefficients [Formula: see text] of the Bergman function expansion for the Hartogs domain [Formula: see text] in a momentum profile [Formula: see text]. Second, using explicit expressions of [Formula: see text], we obtain necessary and sufficient conditions for the coefficients [Formula: see text] to be constants. Finally, we obtain all the invariant complete Kähler metrics on Cartan–Hartogs domains such that their the coefficients [Formula: see text] of the Bergman function expansions are constants.
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Lazaroiu, Calin Iuliu, Daniel McNamee, and Christian Sämann. "Generalized Berezin quantization, Bergman metrics and fuzzy laplacians." Journal of High Energy Physics 2008, no. 09 (September 10, 2008): 059. http://dx.doi.org/10.1088/1126-6708/2008/09/059.

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Loi, Andrea, and Fabio Zuddas. "Partially regular and cscK metrics." International Journal of Mathematics 31, no. 10 (July 27, 2020): 2050079. http://dx.doi.org/10.1142/s0129167x20500792.

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A Kähler metric [Formula: see text] with integral Kähler form is said to be partially regular if the partial Bergman kernel associated to [Formula: see text] is a positive constant for all integer [Formula: see text] sufficiently large. The aim of this paper is to prove that for all [Formula: see text] there exists an [Formula: see text]-dimensional complex manifold equipped with strictly partially regular and cscK metric [Formula: see text]. Further, for [Formula: see text], the (constant) scalar curvature of [Formula: see text] can be chosen to be zero, positive or negative.
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Dissertations / Theses on the topic "Bergman metrics"

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MOSSA, ROBERTO. "Balanced metrics on complex vector bundles and the diastatic exponential of a symmetric space." Doctoral thesis, Università degli Studi di Cagliari, 2011. http://hdl.handle.net/11584/266274.

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This thesis deals with two different subjects: balanced metrics on complex vector bundles and the diastatic exponential of a symmetric space. Correspondingly we have two main results. In the first one we prove that if a holomorphic vector bundle E over a compact Kähler manifold (M,ω) admits a ω-balanced metric then this metric is unique. In the second one, after defining the diastatic exponential of a real analytic Kähler manifold, we prove that for every point p of an Hermitian symmetric space of noncompact type there exists a globally defined diastatic exponential centered in p which is a diffeomorphism and it is uniquely determined by its restriction to polydisks.
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Lazzari, Dalila. "Nuclei Riproducenti." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020.

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La tesi si articola in quattro capitoli. Nel primo capitolo vengono esposti i concetti di base su cui è basata la teoria principale. Inizieremo ricordando le definizioni e i teoremi più rilevanti sugli spazi di Hilbert, sui sistemi ortonormali e sulle funzioni olomorfe per poi arrivare al prodotto Wedge, agli operatori bilineari e al prodotto tensoriale. Il secondo capitolo è destinato ai nuclei riproducenti. Vedremo dapprima la definizione e il Teorema di Aronszajn-Bergman che determina una condizione necessaria e sufficiente sugli spazi affinchè abbiano nucleo riproducente. Studieremo poi le proprietà degli spazi dotati di tale nucleo. Nel terzo capitolo viene illustrato il nucleo di Bergman. Partiremo cercando una stima dell'integrale sui polidischi di C^n di funzioni a quadrato integrabile per poi analizzare il sottospazio generato dalle funzioni olomorfe a quadrato integrabile. Vedremo poi che i risultati ottenuti integrando con la misura di Lebesgue su C^n valgono anche integrando con una misura con peso. Nel quarto ed ultimo capitolo arriveremo al punto saliente della trattazione. Determineremo il proiettore ortogonale dallo spazio delle funzioni a quadrato integrabile allo spazio delle funioni olomorfe a quadrato integrabile e, sotto certe condizioni, prenderemo una determinazione di logaritmo di queste ultime. Grazie alla determinazione di logaritmo costruiremo una forma differenziale hermitiana invariante rispetto agli automorfismi olomorfi dei domini di C^n . Infine, daremo delle ipotesi sotto le quali la forma hermitiana è definita positiva: arriveremo così a definire la metrica che ne deriva. Essa sarà la metrica di Bergman.
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Klevtsov, Semyon. "Bergman kernel, balanced metrics and black holes." 2009. http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000051849.

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Ghara, Soumitra. "Decomposition of the tensor product of Hilbert modules via the jet construction and weakly homogeneous operators." Thesis, 2018. https://etd.iisc.ac.in/handle/2005/4909.

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Let ­½ Cm be a bounded domain and K :­£­!C be a sesqui-analytic function. We show that if ®,¯ È 0 be such that the functions K® and K¯, defined on ­£­, are non-negative definite kernels, then theMm(C) valued function K(®,¯)(z,w) :Æ K®Å¯(z,w) ³ ¡ @i¯@ j logK ¢ (z,w) ´m i , jÆ1 , z,w 2­, is also a non-negative definite kernel on ­£­. Then a realization of the Hilbert space (H,K(®,¯)) determined by the kernel K(®,¯) in terms of the tensor product (H,K®)­(H,K¯) is obtained. For two reproducing kernel Hilbert modules (H,K1) and (H,K2), let An, n ¸ 0, be the submodule of the Hilbert module (H,K1)­(H,K2) consisting of functions vanishing to order n on the diagonal set ¢ :Æ {(z, z) : z 2­}. Setting S0 ÆA? 0 , Sn ÆAn¡1ªAn, n ¸ 1, leads to a natural decomposition of (H,K1)­(H,K2) into infinite direct sum L1 nÆ0Sn. A theorem of Aronszajn shows that the module S0 is isomorphic to the push-forward of the module (H,K1K2) under the map ¶ : ­!­£­, where ¶(z) Æ (z, z), z 2 ­. We prove that if K1 Æ K® and K2 Æ K¯, then the module S1 is isomorphic to the push-forward of the module (H,K(®,¯)) under the map ¶. Let Möb denote the group of all biholomorphic automorphisms of the unit disc D. An operator T in B(H) is said to be weakly homogeneous if ¾(T ) µ ¯D and '(T ) is similar to T for each ' inMöb. For a sharp non-negative definite kernel K : D£D!Mk(C), we show that the multiplication operator Mz on (H,K) is weakly homogeneous if and only if for each ' in Möb, there exists a g' 2Hol(D,GLk(C)) such that the weighted composition operator Mg'C'¡1 is bounded and invertible on (H,K). We also obtain various examples and nonexamples of weakly homogeneous operators in the class FB2(D). Finally, it is shown that there exists a Möbius bounded weakly homogeneous operator which is not similar to any homogeneous operator. We also show that if K1 and K2 are two positive definite kernels on D£D such that the multiplication operators Mz on the corresponding reproducing kernel Hilbert spaces are subnormal, then the multiplication operator Mz on the Hilbert space determined by the sum K1ÅK2 need not be subnormal. This settles a recent conjecture of Gregory T. Adams, Nathan S. Feldman and Paul J.McGuire in the negative.
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Trybuła, Maria. "The Bergman kernel function and related topics." Praca doktorska, 2015. https://ruj.uj.edu.pl/xmlui/handle/item/278051.

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Dinew, Żywomir. "Współrzędne reprezentatywne i geometria metryki Bergmana." Praca doktorska, 2010. http://ruj.uj.edu.pl/xmlui/handle/item/38334.

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Blumberg, Sven [Verfasser]. "Das Randverhalten des Bergman-Kerns und der Bergman-Metrik auf lineal konvexen Gebieten endlichen Typs / vorgelegt von Sven Blumberg." 2005. http://d-nb.info/977931056/34.

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Books on the topic "Bergman metrics"

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Krantz, Steven G. Geometric Analysis of the Bergman Kernel and Metric. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7924-6.

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Geometric Analysis of the Bergman Kernel and Metric. Springer, 2013.

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Krantz, Steven G. Geometric Analysis of the Bergman Kernel and Metric. Springer London, Limited, 2013.

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Krantz, Steven G. Geometric Analysis of the Bergman Kernel and Metric. Springer New York, 2016.

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Book chapters on the topic "Bergman metrics"

1

Berman, Robert, and Julien Keller. "Bergman Geodesics." In Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics, 283–302. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-23669-3_8.

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Maurin, Krzysztof. "Kähler Spaces. Bergman Metrics. Harish-Chandra-Cartan Theorem. Siegel Space (once again!)." In The Riemann Legacy, 102–18. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8939-0_6.

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Christ, Michael. "Upper Bounds for Bergman Kernels Associated to Positive Line Bundles with Smooth Hermitian Metrics." In Algebraic and Analytic Microlocal Analysis, 437–57. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01588-6_8.

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Korányi, Adam. "Bergman Kernel and Bergman Metric." In Analysis and Geometry on Complex Homogeneous Domains, 187–91. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1366-6_13.

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Krantz, Steven G. "The Bergman Metric." In Graduate Texts in Mathematics, 71–85. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7924-6_2.

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Krantz, Steven G. "The Bergman Metric." In Springer Monographs in Mathematics, 195–211. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-63231-5_7.

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Greene, Robert E., Kang-Tae Kim, and Steven G. Krantz. "The Bergman Kernel and Metric." In The Geometry of Complex Domains, 65–98. Boston: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-4622-6_3.

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Krantz, Steven G. "Curvature of the Bergman Metric." In Graduate Texts in Mathematics, 251–71. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7924-6_7.

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Herbort, Gregor. "On the Bergman metric near a plurisubharmonic barrier point." In Complex Analysis and Geometry, 123–32. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8436-5_7.

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Ohsawa, Takeo. "An Essay on the Bergman Metric and Balanced Domains." In Reproducing Kernels and their Applications, 141–48. Boston, MA: Springer US, 1999. http://dx.doi.org/10.1007/978-1-4757-2987-0_13.

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