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Article overview
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Smooth compactness of $f$-minimal hypersurfaces with bounded $f$-index | | Ezequiel Barbosa
; Ben Sharp
; Yong Wei
; | | Date: |
6 Mar 2015 | | Abstract: | Let $(M^{n+1},g,e^{-f}dmu)$ be a complete smooth metric measure space with
$2leq nleq 6$ and Bakry-’{E}mery Ricci curvature bounded below by a positive
constant. We prove a smooth compactness theorem for the space of complete
embedded $f$-minimal hypersurfaces in $M$ with uniform upper bounds on
$f$-index and weighted volume. As a corollary, we obtain a smooth compactness
theorem for the space of embedded self-shrinkers in $mathbb{R}^{n+1}$ with
$2leq nleq 6$. We also prove some estimates on the $f$-index of $f$-minimal
hypersurfaces, and give a conformal structure of $f$-minimal surface with
finite $f$-index in three-dimensional smooth metric measure space. | | Source: | arXiv, 1503.1945 | | Services: | Forum | Review | PDF | Favorites | |
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