Repulsive Curves and Surfaces

Abstract: Repulsive Curves and Surfaces

I am going to report on recent work on the numerical optimization of tangent-point energies of curves and surfaces. After a motivation and brief introduction to the central computational tools (construction of suitable Riemannian metrics on the space of embedded manifolds, a polyhedral discretization of the energies, and fast multipole techniques), I am going to show a couple of numerical results. Not much about the shape of minimizers has been know so far. So, for the first time, we will be able to admire the beauty of the energies' minimizers and gradient flows.

This is based on joint work with Philipp Reiter (Chemnitz University of Technology) and Caleb Brakensiek, Keenan Crane, and Chris Yu (Carnegie Mellon University, Pittsburgh).

graphicsanalysis of PDEsclassical analysis and ODEsdifferential geometryfunctional analysisnumerical analysisoptimization and control

Audience: learners

( paper )

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Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php

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