
Recent Posts
 Why is a² + b² ≥ 2ab ?
 A remark on the divergence theorem
 The CauchySchwarz inequality and the Lagrange identity
 On the existence of a metric compatible with a given connection
 A curious identity on the median triangle
 27 lines on a smooth cubic surface
 Weighted HsiungMinkowski formulas and rigidity of umbilic hypersurfaces
 The discrete GaussBonnet theorem
 Why a vector field rotates about its curl?
 A functional inequality on the boundary of static manifolds
Meta
Recent Comments
tong cheung yu on On the existence of a metric c… Marco Barchiesi on Simple curves with a positive… tong cheung yu on Toric perspective 1 lamwk on Why is a² + b² ≥ 2ab ? Maurice OReilly on Spherical cosine law KKK on Sobolev and Isoperimetric… Anonymous on Sobolev and Isoperimetric… tong cheung yu on On the existence of a metric c… Anonymous on Closed subspaces of a reflexiv… KKK on A curious identity on the medi… Categories
 Algebra
 Algebraic geometry
 Analysis
 Applied mathematics
 Calculus
 Combinatorics
 Complex analysis
 Differential equations
 Discrete Mathematics
 Dynamical system
 Fourier analysis
 Functional analysis
 General Relativity
 Geometry
 Group theory
 Inequalities
 Linear Algebra
 Miscellaneous
 Number Theory
 Operator Theory
 Optimization
 Potential theory
 Probability
 Set Theory
 Statistics
 Topology
 Uncategorized
Top Posts
 Martingale Theory II: Conditional expectation
 Complex analysis  Problem solving strategies.
 Do join us!
 Mean value properties for harmonic functions on Riemannian manifolds
 A note on Obata's theorem
 Mathematics behind JPEG
 Understanding Lagrange multipliers (1)
 The BrunnMinkowski inequality and the isoperimetric inequality
 About
 Why does a mirror reverse left and right, but not top and bottom?
Archives
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
Leave a comment
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
Leave a comment
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
Leave a comment