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

Published 3 Jan 2019 in math.DG | (1901.00944v2)

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.

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