An area bound for surfaces in Riemannian manifolds

Victor Bangert; Ernst Kuwert

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arXiv · 1907.03457

An area bound for surfaces in Riemannian manifolds

Victor Bangert·Ernst Kuwert

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Abstract

Let $M$ 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 $M$ 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.

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Victor Bangert, Ernst Kuwert. 2022-08-17. An area bound for surfaces in Riemannian manifolds. https://arxiv.org/abs/1907.03457

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