Index Estimates for Surfaces with Constant Mean Curvature in 3-dimensional Manifolds

2019/01/03 by Aiex, Nicolau S., Hong, Han
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.00944

Abstract

We prove index estimates for closed and free boundary CMC surfaces in certain 3-dimensional submanifolds of some Euclidean space. When the mean curvature is large enough we are able to prove that the index of a CMC surface in an arbitrary 3-manifold is bounded below by a linear function of its genus.

Related

• Index estimates for constant mean curvature surfaces in three-manifolds by energy comparison
• On the genus and area of constant mean curvature surfaces with bounded\n index
• Lower bounds for the index of compact constant mean curvature surfaces in \mathbb R³ and \mathbb S³
• Geometry of CMC surfaces of finite index
• On the Index of Constant Mean Curvature Hypersurfaces