An area bound for surfaces in Riemannian manifolds
Differential Geometry
2025-02-03 v3
Abstract
Let be a compact Riemannian manifold not containing any totally geodesic surface. Our main result shows that then the area of any complete surface immersed into is bounded by a multiple of its extrinsic curvature energy, i.e. by a multiple of the integral of the squared norm of its second fundamental form.
Cite
@article{arxiv.1907.03457,
title = {An area bound for surfaces in Riemannian manifolds},
author = {Victor Bangert and Ernst Kuwert},
journal= {arXiv preprint arXiv:1907.03457},
year = {2025}
}