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"Geometric measure theory is for those who like their surfaces so rough, that they tie you up and suffocate you." Motivation : Minimal surfaces. One of the central and motivating problems in geometric measure theory is the theory of minimal surfaces. Geometric features of the Allen–Cahn equation (Summer 2019) . Notes from a course I gave at a Princeton RTG summer school. Last updated June 26, 2019. See also an earlier version from a 2018 UConn summer school.. Minimal surfaces and scalar curvature (Summer 2019) . Notes from a mini-course I gave at a 2019 CIMAT (in Guanajuato, Mexico) conference on scalar curvature and relativity.
W.K. ALLARD: On the first variation of area and generalized mean curvature.- F.J. ALMGREN Jr.: Geometric measure theory and elliptic variational problems. In mathematics, geometric measure theory (GMT) is the study of geometric properties of sets (typically in Euclidean space) through measure theory. It allows mathematicians to extend tools from differential geometry to a much larger class of surfaces that are not necessarily smooth. ... Variational Principles in Topology ( Multidimensional Minimal Surface Theory) ...
F.J. ALMGREN Jr.: Geometric measure theory and elliptic variational problems.- E. GIUSTI: Minimal surfaces with obstacles.- J. GUCKENHEIMER: Singularities in soap-bubble-like and soap-film-like surfaces.- D. KINDERLEHRER: The analyticity of the coincidence set in variational inequalities.- 22/08/2000 · Geometric measure theory has become increasingly essential to geometry as well as numerous and varied physical applications. The third edition of this leading text/reference introduces the theory, the framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy.
... among faculty who work in geometry include Ricci and mean curvature flows and other curvature equations, minimal surfaces and geometric measure theory, ... ... General Relativity - Geometric Measure Theory - Geometric Flows Teaching ... to appear [Journal] [arXiv] - Minimal surfaces and the Allen-Cahn equation on ...
Mar 16, 2020 ... A Geometric Measure Theory Approach to Identify Complex Structural Features of Soft Matter Surfaces.