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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Liouville Properties on gradient shrinking Ricci solitons with constant scalar curvature
常标量 曲率梯度收缩 Ricci孤子 Liouville性质
2023/11/13
In this talk we show that bounded harmonic functions are constant on gradient shrinking Ricci solitons with CSC by frequency function method. As an application, we show that the space of harmonic func...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Researches on manifolds with scalar curvature bounded from below
标量曲率 有界 流形
2023/4/25
The motivation to study manifolds with scalar curvature bounded from below comes from Mathematical General Relativity and Riemannian Geometry. In this talk, I'll first briefly introduce some problems ...
Warped product Einstein metrics over spaces with constant scalar curvature
Warped product Einstein metrics spaces constant scalar curvature
2011/2/21
In this paper we study warped product Einstein metrics over spaces with constant scalar curvature. We call such a manifold rigid if the universal cover of the base is Einstein or is isometric to a pro...
Algebraic classification of spacetimes using discriminating scalar curvature invariants
Algebraic classification of spacetimes discriminating scalar curvature invariants
2010/12/27
The Weyl and Ricci tensors can be algebraically classified in a Lorentzian spacetime of arbitrary dimensions using alignment theory. Used in tandem with the boost weight decomposition and curvature op...
Positive scalar curvature, K-area and essentialness
Positive scalar curvature K-area essentialness
2010/11/23
The Lichnerowicz formula yields an index theoretic obstruction to positive scalar curvature metrics on closed spin manifolds. The most general form of this obstruction is due to Rosenberg and takes va...
Algebraic classification of spacetimes using discriminating scalar curvature invariants
Algebraic classification of spacetimes discriminating scalar curvature invariants
2010/12/20
The Weyl tensor and the Ricci tensor can be algebraically classi ed in a Lorentzian spacetime of arbitrary dimensions using alignment the-ory. Used in tandem with the boost weight decomposition and cu...
Scalar curvature and asymptotic Chow stability of projective bundles and blowups
Scalar curvature asymptotic Chow stability projective bundles blowups
2010/12/14
The holomorphic invariants introduced by Futaki as obstruction to the asymptotic Chow semistability are studied by an algebraic-geometric point of view and are shown to be the
Mumford weights of suit...
Constant Scalar Curvature Metrics on Boundary Complexes of Cyclic Polytopes
Regge, Einstein-Hilbert, piecewise
2010/12/7
In [7], a notion of constant scalar curvature metrics on piecewise at manifolds is de ned. Such metrics are candidates for canonical metrics on discrete manifolds. In this paper, we de ne a class of v...
A one parameter family of retarded linear operators on scalar fields on causal sets is introduced. When the causal set is well-approximated by 4 dimensional Minkowski spacetime, the operators are Lore...
Rigidity Theorem of Hypersurfaces with Constant Scalar Curvature in a Unit Sphere
principal curvature Clifford torus Gauss equations
2007/12/12
In this paper, we give a characterization of tori $S^1\left(\sqrt{\frac{nr+2-n}{nr}}\right)\times S^{n-1}\left(\sqrt{\frac{n-2}{nr}}\right)$ and $S^m\left(\sqrt{\frac{m}{n}}\right)\times S^{n-m}\left(...