Minimal surfaces in the round n-sphere are prominent examples of surfaces critical for the Willmore bending energy W; those of low area provide candidates for W-minimizers. To understand when such surfaces are W-stable, we study the interplay between the spectra of their Laplace-Beltrami, area-Jacobi and W-Jacobi operators. We use this to prove: 1) the square Clifford torus in the 3-sphere is the only W-minimizer among 2-tori in the n-sphere; 2) the hexagonal Itoh-Montiel-Ros torus in the 5-sphere is the only other W-stable minimal 2-torus in the n-sphere, for all n; 3) the Itoh-Montiel-...

# Differential Geometry & Geometric Analysis Seminar

The Differential Geometry and Geometry Analysis seminar sees talks most often about interactions between elliptic PDE's and differential geometry. Common topics include (but are not limited to) conformal geometry, minimal surfaces and other variational problems, K\"ahler geometry, CR geometry, elliptic problems from general relativity, nonlinear and/or nonlocal elliptic or parabolic PDE's, and geometric functional inequalities.

Organizer(s):

For more information about this seminar, contact Otis Chodosh or Daniel Ketover.

**Please click on seminar title for complete abstract.**

October 19, 2017

4:30pm - 5:30pm

##### Willmore Stability of Minimal Surfaces in Spheres

Location

Fine Hall 110

Speaker: Rob Kusner,

University of Massachusetts at Amherst

University of Massachusetts at Amherst