Capillary surfaces inside polyhedral regions

TL;DR

This paper introduces a broad new class of embedded capillary surfaces within polyhedral regions, allowing for prescribed contact angles between 1/2a0anda0aa0, which can differ across boundary components.

Contribution

It constructs a large family of embedded capillary surfaces with variable contact angles inside polyhedral regions, expanding the known solutions in geometric analysis.

Findings

Constructed new embedded capillary surfaces with prescribed contact angles.

Allowed contact angles to vary between boundary components.

Extended the class of known solutions in capillarity problems.

Abstract

In this paper we provide a large new family of embedded capillary surfaces inside polyhedral regions in the Euclidean space. The angle of contact of the examples we furnish is prescribed to be any value in $(\frac{\pi}{2}, \pi]$ and it is allowed to vary from one boundary component to the other.