CMC hypersurfaces with bounded Morse index

Ben Sharp; Giuseppe Tinaglia; Theodora Bourni

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CMC hypersurfaces with bounded Morse index

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arxiv 2102.02651 v3 pith:64UJV7X6 submitted 2021-02-04 math.DG

CMC hypersurfaces with bounded Morse index

Theodora Bourni , Ben Sharp , Giuseppe Tinaglia This is my paper

classification math.DG

keywords boundedindexareahypersurfacesmorsealwaysblow-upsbound

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We develop a bubble-compactness theory for embedded CMC hypersurfaces with bounded index and area inside closed Riemannian manifolds in low dimensions. In particular we show that convergence always occurs with multiplicity one, which implies that the minimal blow-ups (bubbles) are all catenoids. We also provide bounds on the area of separating CMC surfaces of bounded (Morse) index and use this, together with the previous results, to bound their genus.

CMC hypersurfaces with bounded Morse index

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