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Published: 9 March 2023
Last updated: 10 March 2023

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1

1931-, Colares A. Gervasio, ed. Minimal surfaces in IR³. Berlin: Springer-Verlag, 1986.

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2

P, Minicozzi William, ed. A course in minimal surfaces. Providence, R.I: American Mathematical Society, 2011.

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3

Hitchin, N. J. Monopoles, minimal surfaces, and algebraic curves. Montréal, Québec, Canada: Presses de l'Université de Montréal, 1987.

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4

Stefan, Hildebrandt, and Tromba Anthony, eds. Global analysis of minimal surfaces. 2nd ed. Heidelberg: Springer, 2010.

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5

Paul, Krée, ed. Ennio de Giorgi Colloquium. Boston: Pitman Advanced Pub. Program, 1985.

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6

Conference on Multigrid Methods (2nd 1985 Cologne, Germany). Multigrid methods II: Proceedings of the 2nd European Conference on Multigrid Methods, held at Cologne, October 1-4, 1985. Berlin: Springer-Verlag, 1986.

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7

1966-, Pérez Joaquín, and Galvez José A. 1972-, eds. Geometric analysis: Partial differential equations and surfaces : UIMP-RSME Santaló Summer School geometric analysis, June 28-July 2, 2010, University of Granada, Granada, Spain. Providence, R.I: American Mathematical Society, 2012.

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8

author, Tkachev Vladimir 1963, and Vlăduț, S. G. (Serge G.), 1954- author, eds. Nonlinear elliptic equations and nonassociative algebras. Providence, Rhode Island: American Mathematical Society, 2014.

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9

Southeast Geometry Seminar (15th 2009 University of Alabama at Birmingham). Geometric analysis, mathematical relativity, and nonlinear partial differential equations: Southeast Geometry Seminars Emory University, Georgia Institute of Technology, University of Alabama, Birmingham, and the University of Tennessee, 2009-2011. Edited by Ghomi Mohammad 1969-. Providence, Rhode Island: American Mathematical Society, 2013.

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10

Mann, Peter. Constrained Lagrangian Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0008.

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This chapter builds on the previous two chapters to tackle constrained systems, using Lagrangian mechanics and constrained variations. The first section deals with holonomic constraint equations using Lagrange multipliers; these can be used to reduce the number of coordinates until a linearly independent minimal set is obtained that describes a constraint surface within configuration space, so that Lagrange equations can be set up and solved. Motion is understood to be confined to a constraint submanifold. The variational formulation of non-holonomic constraints is then discussed to derive the vakonomic formulation. These erroneous equations are then compared to the central Lagrange equation, and the precise nature of the variations used in each formulation is investigated. The vakonomic equations are then presented in their Suslov form (Suslov–vakonomic form) in an attempt to reconcile the two approaches. In addition, the structure of biological membranes is framed as a constrained optimisation problem.
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11

Küster, Albrecht, Stefan Hildebrandt, and Ulrich Dierkes. Regularity of Minimal Surfaces. Springer, 2010.

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12

Regularity Of Minimal Surfaces. Springer, 2010.

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13

Regularity of Minimal Surfaces. Springer, 2010.

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14

Global Analysis of Minimal Surfaces. Springer, 2010.

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15

Henriksen, Niels Engholm, and Flemming Yssing Hansen. Potential Energy Surfaces. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805014.003.0003.

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This chapter discusses potential energy surfaces, that is, the electronic energy as a function of the internuclear coordinates as obtained from the electronic Schrödinger equation. It focuses on the general topology of such energy surfaces for unimolecular and bimolecular reactions. To that end, concepts like saddle point, barrier height, minimum-energy path, and early and late barriers are discussed. It concludes with a discussion of approximate analytical solutions to the electronic Schrödinger equation, in particular, the interaction of three hydrogen atoms expressed in terms of Coulomb and exchange integrals, as described by the so-called London equation. From this equation it is concluded that the total electronic energy is not equal to the sum of H–H pair energies. Finally, a semi-empirical extension of the London equation—the LEPS method—allows for a simple but somewhat crude construction of potential energy surfaces.
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16

Садовников, Василий. Теория гетерогенного катализа. Теория хемосорбции. Publishing House Triumph, 2021. http://dx.doi.org/10.32986/978-5-40-10-01-2001.

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This monograph is a continuation of the monograph by V.V. Sadovnikov. Lateral interaction. Moscow 2006. Publishing house "Anta-Eco", 2006. ISBN 5-9730-0017-6. In this work, the foundations of the theory of heterogeneous catalysis and the theory of chemisorption are more easily formulated. The book consists of two parts, closely related to each other. These are the theoretical foundations of heterogeneous catalysis and chemisorption. In the theory of heterogeneous catalysis, an experiment is described in detail, which must be carried out in order to isolate the stages of a catalytic reaction, to find the stoichiometry of each of the stages. This experiment is based on the need to obtain the exact value of the specific surface area of the catalyst, the number of centers at which the reaction proceeds, and the output curves of each of the reaction products. The procedures for obtaining this data are described in detail. Equations are proposed and solved that allow calculating the kinetic parameters of the nonequilibrium stage and the thermodynamic parameters of the equilibrium stage. The description of the quantitative theory of chemisorption is based on the description of the motion of an atom along a crystal face. The axioms on which this mathematics should be based are formulated, the mathematical apparatus of the theory is written and the most detailed instructions on how to use it are presented. The first axiom: an atom, moving along the surface, is present only in places with minima of potential energy. The second axiom: the face of an atom is divided into cells, and the position of the atom on the surface of the face is set by one parameter: the cell number. The third axiom: the atom interacts with the surrounding material bodies only at the points of minimum potential energy. The fourth axiom: the solution of the equations is a map of the arrangement of atoms on the surface. The fifth axiom: quantitative equations are based on the concept of a statistically independent particle. The formation energies of these particles and their concentration are calculated by the developed program. The program based on these axioms allows you to simulate and calculate the interaction energies of atoms on any crystal face. The monograph is intended for students, post-graduate students and researchers studying work and working in petrochemistry and oil refining.
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17

Pierre, Michel, and Antoine Henrot. Variation et optimisation de formes: Une analyse géométrique (Mathématiques et Applications). Springer, 2007.

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18

Shape Variation and Optimization: A Geometrical Analysis. American Mathematical Society, 2018.

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