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Compactness of minimal hypersurfaces with bounded index. (English) Zbl 1390.53065

The author proves an interesting compactness result for minimal hypersurfaces with bounded index and volume (Theorem 2.3), which can be thought of as an extension of the compactness theorem of H. I. Choi and R. Schoen [Invent. Math. 81, 387–394 (1985; Zbl 0577.53044)] to higher dimensions.

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
58E10 Variational problems in applications to the theory of geodesics (problems in one independent variable)

Citations:

Zbl 0577.53044
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