Geometric Analysis Seminar —— A Simon-Smith min-max theory for anisotropic minimal surfaces with genus bound
报告人：汪铃(Bocconi University, Italy)
时间：2026-08-11 10:00-11:00
地点：智华楼312
【摘要】
In this talk, I will discuss a Simon–Smith min-max theory for anisotropic minimal surfaces in closed three-manifolds, with controlled genus. The starting point is an anisotropic analogue of the celebrated theorem of Meeks–Simon–Yau: every minimizing sequence of surfaces within a fixed isotopy class converges, as varifolds, to a smooth stable anisotropic minimal surface, possibly with multiplicity, with lower semicontinuity of genus. This result strengthens previous existence theorems for anisotropic Plateau problems and provides the compactness needed for a topological min-max construction. As an application, we prove the existence of closed embedded anisotropic minimal surfaces with controlled genus in arbitrary closed three-manifolds. This is joint work with Antonio De Rosa and Aria Halavati.
