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 27 lines on a smooth cubic surface
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Category Archives: General Relativity
Weighted HsiungMinkowski formulas and rigidity of umbilic hypersurfaces
1. Motivation and Main Results A. D. Alexandrov [Ale1956], [Ale1962] proved that the only closed hypersurfaces of constant (higher order) mean curvature embedded in are round hyperspheres. The embeddedness assumption is essential. For instance, admits immersed tori with constant mean … Continue reading
Posted in Calculus, General Relativity, Geometry, Inequalities
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A functional inequality on the boundary of static manifolds
1. introduction and statement of results The research in this article is largely motivated by the following result concerning a functional inequality on the boundary of bounded domains in the Euclidean space , proved in [MTX] Corollary 3.1. Theorem 1 … Continue reading
Posted in Calculus, General Relativity, Geometry, Inequalities
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A positive mass theorem and Penrose type inequalities for the GaussBonnetChern mass
In a recent preprint [GWW1], Ge, Wang and Wu proposed a family of new masses () for an asymptotically flat manifold and proved a positive mass theorem and some Penrose type inequalities for graphs, at least when . They remarked … Continue reading
Posted in Calculus, General Relativity, Geometry, Inequalities
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