Geometric Analysis and Topology Seminar

---

Existence of free boundary constant mean curvature disks

Speaker: Darong Cheng, University of Miami

Location: Warren Weaver Hall 512

Date: Friday, November 11, 2022, 11 a.m.

Synopsis:

Given a surface S in R³, a classical problem is to find a disk-type surface with prescribed constant mean curvature whose boundary meets S orthogonally. When S is diffeomorphic to a sphere, direct minimization could lead to trivial solutions and hence min-max constructions are needed. Among the earlier such constructions is the work of Struwe, who produced the desired surfaces for almost every mean curvature value up to that of the smallest round sphere enclosing S. 

In a joint work with Xin Zhou (Cornell), we combined Struwe’s method with other techniques to produce constant mean curvature 2-spheres in Riemannian 3-spheres. In this talk, I will report on more recent progress where the ideas in that work are applied back to the free boundary problem to refine and improve Struwe’s result.