Communications in Analysis and Geometry

Volume 30 (2022)

Number 10

Refined position estimates for surfaces of Willmore type in Riemannian manifolds

Pages: 2315 – 2346



Jan Metzger (Institute for Mathematics, University of Potsdam, Germany)


In this paper we consider surfaces which are critical points of the Willmore functional subject to constrained area. In the case of small area we calculate the corrections to the intrinsic geometry induced by the ambient curvature. These estimates together with the choice of an adapted geometric center of mass lead to refined position estimates in relation to the scalar curvature of the ambient manifold.

The author’s research was supported by the DFG, in the form of grant ME 3816/1-2.

Received 4 May 2020

Accepted 22 July 2020

Published 29 September 2023