Calculus of Variations and Geometric Measure Theory

Y. R. Y. Zhang - A. Figalli

Strong stability for the Wulff inequality with a crystalline norm

created by figalli on 02 Apr 2020
modified on 10 Feb 2023


Published Paper

Inserted: 2 apr 2020
Last Updated: 10 feb 2023

Journal: Comm. Pure Appl. Math.
Year: 2020


Let K be a convex polyhedron and F its Wul energy, and let C (K) denote the set of convex polyhedra close to K whose faces are parallel to those of K. We show that, for suciently small , all -minimizers belong to C (K). As a consequence of this result we obtain the following sharp stability inequality for crystalline norms: There exist = (K; n) > 0 and  = (K; n) > 0 such that, whenever jEj = jKj and jEKj   then F(E)