Results 11 to 20 of about 1,358 (218)
Width, Ricci curvature, and minimal hypersurfaces [PDF]
Journal of Differential Geometry, 2017 Let $(M,g_0)$ be a closed Riemannian manifold of dimension $n$, for $3 \leq n \leq 7$, and non-negative Ricci curvature. Let $g = ^2 g_0$ be a metric in the conformal class of $g_0$. We show that there exists a smooth closed embedded minimal hypersurface in $(M,g)$ of volume bounded by $C V^{\frac{n-1}{n}}$, where $V$ is the total volume of $(M,g ...
Parker Glynn-Adey, Yevgeny Liokumovich
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Minimal Conformally Flat Hypersurfaces [PDF]
The Journal of Geometric Analysis, 2018 We study conformally flat hypersurfaces $f\colon M^{3} \to \Q^{4}(c)$ with three distinct principal curvatures and constant mean curvature $H$ in a space form with constant sectional curvature $c$. First we extend a theorem due to Defever when $c=0$ and show that there is no such hypersurface if $H\neq 0$. Our main results are for the minimal case $H=0$
do Rei Filho, C., Tojeiro, R.
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Minimal Hypersurfaces with Arbitrarily Large Area [PDF]
International Mathematics Research Notices, 2019 Abstract For $3\leq n\leq 7$, we prove that a bumpy closed Riemannian $n$-manifold contains a sequence of connected embedded closed minimal surfaces with unbounded area.
Otis Chodosh, Christos Mantoulidis
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Stable H-Minimal Hypersurfaces [PDF]
The Journal of Geometric Analysis, 2013 34 ...
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Generic scarring for minimal hypersurfaces along stable hypersurfaces [PDF]
Geometric and Functional Analysis, 2021 Let $M^{n+1}$ be a closed manifold of dimension $3\leq n+1\leq 7$. We show that for a $C^\infty$-generic metric $g$ on $M$, to any connected, closed, embedded, $2$-sided, stable, minimal hypersurface $S\subset (M,g)$ corresponds a sequence of closed, embedded, minimal hypersurfaces $\{ _k\}$ scarring along $S$, in the sense that the area and Morse ...
Song, Antoine, Zhou, Xin
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Minimal Hypersurfaces with Finite Index [PDF]
Mathematical Research Letters, 2002 The main result of this paper is the following: Let \(M=M^n\) be a complete immersed oriented minimal hypersurface in \({\mathbb R}^{n+1}\) with \(n \geq 3\). Suppose \(M\) has finite index. Then \(M\) must have finite first \(L^2\)-Betti number, i.e. \(\dim H^1(L^2(M)) < \infty\). In particular, \(M\) must have finitely many ends.
Li, Peter, Wang, Jiaping
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On Minimal Hypersurfaces of a Unit Sphere
Mathematics, 2021 Minimal compact hypersurface in the unit sphere Sn+1 having squared length of shape operator A22), provided the scalar curvature τ is a constant on integral curves of w.
Amira Ishan +3 more
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Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 1983 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Karliğa, B., Hacisalihoğlu, H. H.
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Rigidity of Complete Minimal Submanifolds in Spheres
Frontiers in Physics, 2020 Let M be an n-dimensional complete minimal submanifold in an (n + p)-dimensional sphere 𝕊n+p, and let h be the second fundamental form of M. In this paper, it is shown that M is totally geodesic if the L2 norm of |h| on any geodesic ball of M is of less ...
Jundong Zhou, Jundong Zhou
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On minimal homothetical hypersurfaces [PDF]
Colloquium Mathematicum, 2007 We give a classification of minimal homothetical hypersurfaces in an (n + 1)-dimensional Euclidean space. In fact, when n 3, a minimal homothetical hyper- surface is a hyperplane, a quadratic cone, a cylinder on a quadratic cone or a cylinder on a helicoid.
Lin Jiu, Huafei Sun
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