A new proof of the Willmore inequality via a divergence inequality
Abstract
We present a new proof of the Willmore inequality for an arbitrary bounded domain ⊂Rn with smooth boundary. Our proof is based on a parametric geometric inequality involving the electrostatic potential for the domain ; this geometric inequality is derived from a geometric differential inequality in divergence form. Our parametric geometric inequality also allows us to give new proofs of the quantitative Willmore-type and the weighted Minkowski inequalities by Agostiniani and Mazzieri.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.