Geometry and Geometric Analysis Working Group
Local minimality of strictly stable extremal submanifolds
Speaker: Andrea Marchese, University of Pavia
Location: Warren Weaver Hall 517
Date: Monday, November 26, 2018, 11 a.m.
I will discuss an extension of a result by Brian White, who proved that any smooth, compact submanifold, which is a strictly stable critical point for an elliptic parametric functional, is the unique minimizer in its homology class, if the minimization is constrained to a sufficiently small geodesic tubular neighborhood of the submanifold. We replace the tubular neighborhood with one induced by the flat distance of integral currents and we provide quantitative estimates. The proof is based on the so called "selection principle", which, via a penalization technique, allows us to recast the problem in the class of normal graphs, exploiting the regularity theory for almost minimizers. Joint work with D. Inauen (Zurich).