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Talks at the mathematical institute

Projektseminar Geometrische Analysis

Winter term 2025

Veranstaltungen und Vorträge

Mingwei Zhang:
The curl operator and Sobolev inequalities for differential forms

Time and place

Tuesday, 28.10.25, 16:15-17:45, Seminarraum 125

Abstract

The curl operator for vectors in R^3 is of special importance and gives rise to various Sobolev inequalities. In this talk we will introduce the generalized curl operator for differential forms in higher dimensions and discuss the spectral analysis. As an application, we prove that fundamental bubbles (Killing forms) are local minimizers of one Sobolev inequality, but not local minimizers of another Sobolev inequality. This is a joint work with Prof. Guofang Wang.

Veranstaltungen und Vorträge

Xuwen Zhang:
Anisotropic minimal graphs with free boundary

Time and place

Tuesday, 4.11.25, 16:15-17:45, Seminarraum 125

Abstract

Minimal surface equation is a classical topic in Geometric Analysis and PDEs. In this talk, we discuss recent progress on anisotropic minimal surface equation, and prove the following Liouville-type theorem: any anisotropic minimal graph with free boundary in the half-space must be flat, provided that the graph function has at most one-side linear growth. This is a joint work with Guofang Wang, Wei Wei, and Chao Xia.

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