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Existence of disks with prescribed mean curvature and contact angle in arbitrary codimension
Abstract
Under suitable relative homotopy and boundary admissibility assumptions, we establish a min-max theory in arbitrary codimension that produces nonconstant branched immersed disks or spheres in closed Riemannian manifolds, with controlled Morse index, where the prescribed mean curvature type tensor and the nonorthogonal, nonconstant contact angle condition of disks along a supporting submanifold are determined by the same differential 2-form. In Euclidean space, under suitable topological and convex barrier assumptions, we obtain such disks with free boundary on a closed supporting hypersurface and a Morse index bound depending only on the ambient dimension.
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BibTeX
@misc{gao2026existence,
title = {{Existence of disks with prescribed mean curvature and contact angle in arbitrary codimension}},
author = {Rui Gao and Miaomiao Zhu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28410},
eprint = {2609.28410},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28410},
}
RIS
TY - UNPB
TI - Existence of disks with prescribed mean curvature and contact angle in arbitrary codimension
AU - Rui Gao
AU - Miaomiao Zhu
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28410
UR - https://arxiv.org/abs/2609.28410
AB - Under suitable relative homotopy and boundary admissibility assumptions, we establish a min-max theory in arbitrary codimension that produces nonconstant branched immersed disks or spheres in closed Riemannian manifolds, with controlled Morse index, where the prescribed mean curvature type tensor and the nonorthogonal, nonconstant contact angle condition of disks along a supporting submanifold are determined by the same differential 2-form. In Euclidean space, under suitable topological and convex barrier assumptions, we obtain such disks with free boundary on a closed supporting hypersurface and a Morse index bound depending only on the ambient dimension.
ER -