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arXiv · 2603.18783

Index Estimates for CMC and Minimal Surfaces with Capillary Boundary

Luca Seemungal
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Abstract

We prove that the index of a CMC surface with capillary boundary is bounded from above linearly by its genus, number of boundary components, and branching order, and also by some Willmore-type energy involving the area, mean curvature, contact angle, and ambient curvature. The main auxiliary theorem of more general interest is a comparison of the second variations of area and energy at a branched conformal map with boundary. In the appendix we derive the various second variation formulae for area, enclosed-volume, and wetting functionals away from critical points and for non-admissible variations, the purpose of which is to rather comprehensively fill a gap in the literature.

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Luca Seemungal. 2026-03-19. Index Estimates for CMC and Minimal Surfaces with Capillary Boundary. https://arxiv.org/abs/2603.18783

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