Geometric flows from viewpoint of calculus of variations

Geometric Aspects of Nonlinear Partial Differential Equations

06 October 14:00 - 15:00

Pengfei Guan - McGill University

We discuss flow approach for isoperimetric problems. Given two geometric functionals, one would like to find optimal relationship between them (e.g., classical isoperimetric inequality for volume and surface area). This can be stated as a variational problem: find extremal of one functional with the other constrained. One would like to design flows serving as good paths to the optimal solution. This consideration leads to a new class of interesting curvature flows, mean curvature type and inverse mean curvature type. The longtime existence and convergence are the main focus. We discuss some new results and open problems.
Panagiota Daskalopoulos
Columbia University
Alessio Figalli
ETH Zürich
Erik Lindgren
Uppsala University
Henrik Shahgholian
KTH Royal Institute of Technology
Susanna Terracini,
University of Turin


Erik Lindgren

Henrik Shahgholian


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