Communications in Analysis and Geometry

Volume 29 (2021)

Number 2

A gap theorem for free boundary minimal surfaces in the three-ball

Pages: 283 – 292



Lucas Ambrozio (Mathematics Institute, University of Warwick, Coventry, United Kingdom)

Ivaldo Nunes (Departamento de Matemática, Universidade Federal do Maranhão, São Luís, MA, Brazil)


We show that, among free boundary minimal surfaces in the unit ball in the three-dimensional Euclidean space, the flat equatorial disk and the critical catenoid are characterised by a pinching condition on the length of their second fundamental form.

L. A. was supported by the ERC Start Grant PSC and LMCF 278940. I. N. was supported by CNPq-Brazil and FAPEMA/ CNPq.

Received 21 January 2017

Accepted 22 August 2018

Published 19 April 2021