Calculus of Variations and Geometric Measure Theory

L. De Masi - G. De Philippis

Min-max construction of minimal surfaces with a fixed angle at the boundary

created by dephilipp on 05 Jun 2023



Inserted: 5 jun 2023

Year: 2021

ArXiv: 2111.09913 PDF


We prove the existence of minimal surfaces in a bounded convex subset of $\mathbb R^3$, $\mathcal M$, intersecting the boundary of $\mathcal M$ with a fixed contact angle. The proof is based on a min-max construction in the spirit of Almgren-Pitts for the capillarity functional.