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Critical Points and Morse Theory
1997In this chapter we introduce Morse theory, a systematic way of studying certain features of smooth functions on manifolds. We will primarily consider surfaces and three-manifolds, because the main applications of Morse theory in computer geometry are concentrated in these dimensions.
Anatolij T. Fomenko, Tosiyasu L. Kinii
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The Critical Point: Theory and Experiment
High Temperature, 2001It is demonstrated that the Gibbs concept of the critical state and the equations for the critical point formulated by him make it possible to provide a complete description the peculiarities of the behavior and properties of matter at the critical point.
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Some remarks on nonsmooth critical point theory
Journal of Global Optimization, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Livrea, Roberto, Bisci, Giovanni Molica
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Nonsmooth Critical Point Theory
1999The aim of this chapter is to present general results, many of them belonging to the authors, that can be applied to locally Lipschitz functionals, possibly invariant under a compact Lie group of linear isometries. The nonsmooth critical point theory in the locally Lipschitz case originates in the work of Chang [4].
D. Motreanu, P. D. Panagiotopoulos
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Topics in Critical Point Theory
2012This book introduces the reader to powerful methods of critical point theory and details successful contemporary approaches to many problems, some of which had proved resistant to attack by older methods. Topics covered include Morse theory, critical groups, the minimax principle, various notions of linking, jumping nonlinearities and the Fučík ...
Kanishka Perera, Martin Schechter
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The critical point and scaling theory
Physica, 1974Abstract The origin and physical meaning of the scaling and homogeneity hypotheses in the theory of equilibrium critical phenomena are discussed. The purely thermodynamic critical-point exponent relations, and those that also involve the coherence length, are first derived from separate and apparently unrelated hypotheses.
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The Classical Theory of Critical Points
1994The various methods available for expressing the criteria for a critical point are developed and their equivalence is demonstrated. Some are shown to be more convenient for use than others, especially when dealing with multi-component mixtures. The equations most often used in calculating the critical points in pure fluids or in binary mixtures ...
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Topics on critical point theory
2008Many questions in mathematics and physics can be reduced to the problem of finding and classifying the critical points of a suitable functional on an appropriate manifold. In this thesis, we will be concerned with the problems of existence, location and structure of critical points by building upon the well known min-max methods that are presently used
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