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Local Rigidity Theorems for Minimal Hypersurfaces
The Annals of Mathematics, 1969One purpose of the paper is to determine all minimal hypersurfaces \(M\) of the unit sphere \(S^{n+1}\) satisfying certain additional conditions. Let \(\kappa=\frac 1{n(n-1)} \sum g^{ij}R_{ij}\) be the scalar curvature of \(M\). Let \(M_{k, n-k} = S^k(\sqrt{k/n})\times S^{n-k}(\sqrt{n-k/n})\), where \(S^p(r)= \{x\in\mathbb R^{p+1}\mid \sum x_i^2 =r^2\}\
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Minimal Hypersurfaces in an m-Sphere
Proceedings of the American Mathematical Society, 1971Let \(M\) be an \(n\)-dimensional manifold immersed in a Riemannian manifold \(R^n\) of dimension \(m\). Let \(H\) and \(V\) denote the mean curvature vector and the second fundamental form of \(M\) in \(R^n\). If there exists a function \(f\) on \(M\) which satisfies \(\langle V(X,Y), H\rangle = f(X,Y)\) for all tangent vectors \(X,Y\) on \(M\), then \
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Chern's conjecture on minimal hypersurfaces
Mathematische Zeitschrift, 1998The following conjecture is well-known: Chern's conjecture. For \(n\)-dimensional closed minimal hypersurfaces in the unit sphere \(S^{n+1}(1)\) with constant scalar curvature, the values \(S\) of the squared norm of the second fundamental forms should be discrete. Relating to this conjecture, we prove the following main theorem: Theorem 1. Let \(M^n\)
Yang, Hongcang, Cheng, Qing-Ming
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Photodynamic therapy of cancer: An update
Ca-A Cancer Journal for Clinicians, 2011Patrizia M Agostinis +2 more
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Expectant management for men with early stage prostate cancer
Ca-A Cancer Journal for Clinicians, 2015Mark S Litwin
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Liquid biopsy and minimal residual disease — latest advances and implications for cure
Nature Reviews Clinical Oncology, 2019Klaus Pantel, Catherine Alix-Panabières
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Minimal Length Scale Scenarios for Quantum Gravity
Living Reviews in Relativity, 2013Sabine Hossenfelder
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Comparative genomics, minimal gene-sets and the last universal common ancestor
Nature Reviews Microbiology, 2003Eugene V Koonin
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