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.

Received 20 November 2018

Accepted 12 February 2021

Published 16 July 2024