Publication

The singular set of minimal surfaces near polyhedral cones

2022

Abstract

We adapt the method of Simon [26] to prove a C1;α-regularity theorem for minimal varifolds which resemble a cone C20 over an equiangular geodesic net. For varifold classes admitting a "nohole" condition on the singular set, we additionally establish C1; α- regularity near the cone C20 xRm. Combined with work of Allard [2], Simon [26], Taylor [29], and Naber-Valtorta [21], our result implies a C1; α-structure for the top three strata of minimizing clusters and size-minimizing currents, and a Lipschitz structure on the (n - 3)-stratum.

Official source

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

2022

Abstract

Official source

Related concepts (27)

Minimal surface

In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film, which is a minimal surface whose boundary is the wire frame.

Schwarz minimal surface

In differential geometry, the Schwarz minimal surfaces are periodic minimal surfaces originally described by Hermann Schwarz. In the 1880s Schwarz and his student E. R. Neovius described periodic minimal surfaces. They were later named by Alan Schoen in his seminal report that described the gyroid and other triply periodic minimal surfaces. The surfaces were generated using symmetry arguments: given a solution to Plateau's problem for a polygon, reflections of the surface across the boundary lines also produce valid minimal surfaces that can be continuously joined to the original solution.

Enneper surface

In differential geometry and algebraic geometry, the Enneper surface is a self-intersecting surface that can be described parametrically by: It was introduced by Alfred Enneper in 1864 in connection with minimal surface theory. The Weierstrass–Enneper parameterization is very simple, , and the real parametric form can easily be calculated from it. The surface is conjugate to itself.

Related publications (5)

The singular set of minimal surfaces near polyhedral cones

Chat with Graph Search

Mitigating Membership Inference Vulnerability in Iterative Federated Clustering Algorithm

Unsupervised Pattern Discovery for Mobile Network Tuning Optimization

Spatio-Temporal Analysis of Spontaneous Speech with Microphone Arrays