We prove the existence of minimal surfaces in a bounded convex subset M of R3 intersecting the boundary of 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.
MIN-MAX CONSTRUCTION OF MINIMAL SURFACES WITH A FIXED ANGLE AT THE BOUNDARY
De Philippis G.
2025
Abstract
We prove the existence of minimal surfaces in a bounded convex subset M of R3 intersecting the boundary of 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.
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