Results 71 to 80 of about 736 (175)
Symmetry, Integrability and Geometry: Methods and Applications, 2007 The $(2k)$-th Gauss-Bonnet curvature is a generalization to higher dimensions of the $(2k)$-dimensional Gauss-Bonnet integrand, it coincides with the usual scalar curvature for $k = 1$.
Mohammed Larbi Labbi
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On area comparison and rigidity involving the scalar curvature [PDF]
In this thesis we study the effects of lower bounds for the curvature of a Riemannian manifold M on the geometry and topology of closed, minimal hypersurfaces.
Moraru, Vlad
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Surgery and equivariant Yamabe invariant
, 2006 We consider the equivariant Yamabe problem, i.e., the Yamabe problem on the space of G-invariant metrics for a compact Lie group G. The G-Yamabe invariant is analogously defined as the supremum of the constant scalar curvatures of unit volume G-invariant
Sung, Chanyoung
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The singular CR Yamabe problem and Hausdorff dimension
Communications in Contemporary MathematicsIn this paper, we consider CR analogs of Huber’s theorem for Riemann surfaces. We also investigate the developing map for CR structures that are spherical in the case of three-dimensional CR manifolds and give conditions when this developing map is injective.
Sagun Chanillo, Paul C. Yang
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Some results on the weighted Yamabe problem with or without boundary
. Let (Mn,g,e− ϕdVg,e− ϕdAg,m) be a compact smooth metric measure space with boundary with n ⩾ 3. In this article, we consider several Yamabe-type problems on a compact smooth metric measure space with or without boundary: uniqueness problem on the ...
Ho, Pak Tung;Shin, Jinwoo;Yan, Zetian
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Das Yamabe-Problem auf global-hyperbolischen Lorentz-Mannigfaltigkeiten
, 2020 Im Jahre 1960 behauptete Yamabe folgende Aussage bewiesen zu haben: Auf jeder kompakten Riemannschen Mannigfaltigkeit (M,g) der Dimension n ≥ 3 existiert eine zu g konform äquivalente Metrik mit konstanter Skalarkrümmung. Diese Aussage ist äquivalent zur
Rothe, Viktoria
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The Yamabe flow on asymptotically Euclidean manifolds with nonpositive Yamabe constant
, 2023 24 pagesInternational audienceWe study the Yamabe flow on asymptotically flat manifolds with non-positive Yamabe constant $Y\leq 0$. Previous work by the second and third named authors \cite{ChenWang} showed that while the Yamabe flow always converges in
Carron, Gilles, Wang, Yi, Chen, Eric
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, 2010 Yamabe問題內容如下：給定任何一個三維以上的黎曼緊緻流形，找一個保角的度量使得在此度量之下的純量曲率為一定值。此問題已經被Richard Schoen 在 1984 年完全解決。本論文研究此問題的證明。並且對於此問題的拋物偏微分方程版本， Yamabe 流，在本論文中也收錄了一些相關的結果。The Yamabe problem is as following. Given a compact Riemannian manifold of dimension n≥3, find a conformal
張瑞恩, Chang, Jui-En
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The Yamabe problem with singularities
, 2008 Let $(M,g)$ be a compact Riemannian manifold of dimension $n\geq 3$. Under some assumptions, we prove that there exists a positive function $φ$ solution of the following Yamabe type equation Δφ+ hφ= \tilde h φ^{\frac{n+2}{n-2}} where $h\in L^p(M)$, $p>n/2$ and $\tilde h\in \mathbb R$.
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On Yamabe's problem---by a modified direct method
Tohoku Mathematical Journal, 1982 In this article, the author gives a new proof of T. Aubin's result to the effect that the total scalar curvature functional achieves its infimum in a given conformal class of metrics provided this infimum is less than its value on the standard sphere. The method is more functional analytical in spirit than Aubin's.
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