Communications in Analysis and Geometry

Volume 31 (2023)

Number 5

A note on minimal surfaces with bounded index

Pages: 1069 – 1078

DOI: https://dx.doi.org/10.4310/CAG.2023.v31.n5.a1

Author

Davi Maximo (Department of Mathematics, University of Pennsylvania, Philadelphia, PA, USA)

Abstract

For any closed Riemannian three-manifold, we prove that for any sequence of closed embedded minimal surfaces with uniformly bounded index, the genus can only grow at most linearly with respect to the area.

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Received 20 November 2018

Accepted 12 February 2021

Published 16 July 2024