Minimal hypersurfaces in manifolds of Ricci curvature bounded below

DOI10.1515/CRELLE-2022-0050arXiv2109.02483MaRDI QIDQ6376958

Publication date: 6 September 2021

Abstract: In this paper, we study the angle estimate of distance functions from minimal hypersurfaces in manifolds of Ricci curvature bounded from below using Colding's method in [13]. With Cheeger-Colding theory, we obtain the Laplacian comparison for limits of distance functions from minimal hypersurfaces in the version of Ricci limit space. As an application, if a sequence of minimal hypersurfaces converges to a metric cone

C Y i m e s m a t h b b R^{n - k} (2 l e q k l e q n)

in a non-collapsing metric cone

C X i m e s m a t h b b R^{n - k}

obtained from ambient manifolds of almost nonnegative Ricci curvature, then we can prove a Frankel property for the cross section

Y

of

C Y

. Namely,

Y

has only one connected component in

X

.

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

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