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Curvature properties of pseudo-sphere bundles over paraquaternionic manifolds
twistor space Einstein manifold paraquaternionic structure mixed 3-structure
2011/9/21
Abstract: In this paper we obtain several curvature properties of the twistor and reflector spaces of a paraquaternionic K\"{a}hler manifold and prove the existence of both positive and negative mixed...
Extremal Kahler metrics and energy functionals on projective bundles
Extremal Kahler metrics energy functionals projective bundles
2011/9/21
Abstract: In this paper, we prove the equivalence of the existence of extremal Kahler metrics and the properness of the modified K energy on projective bundles. Moreover, we discuss the relations of t...
Gromov-Lawson-Schoen-Yau theory and isoparametric foliations
Gromov-Lawson-Schoen-Yau theory isoparametric hypersurface positive scalar curvature
2011/9/21
Abstract: Motivated by the celebrated Gromov-Lawson-Schoen-Yau surgery the- ory on metrics of positive scalar curvature, the present paper constructs a double manifold associated with a minimal isopar...
Abstract: We simplify and improve the curvature estimates in the paper: On the conditions to extend Ricci flow(II). Furthermore, we develop some volume estimates for the Ricci flow with bounded scalar...
Abstract: We develop some estimates under the Ricci flow and use these estimates to study the blowup rates of curvatures at singularities. As applications, we obtain some gap theorems:
$\displaystyl...
On the curvature of G-manifolds with finitely many non-principal orbits
G-manifold cohomogeneity Ricci curvature
2011/9/20
Abstract: We investigate the curvature of invariant metrics on G-manifolds with finitely many non-principal orbits. We prove existence results for metrics of positive Ricci curvature and non-negative ...
Local Poincare inequalities from stable curvature conditions on metric spaces
Ricci curvature metric measure spaces geodesics Poincare inequality
2011/9/20
Abstract: We prove local Poincar\'e inequalities under various curvature-dimension conditions which are stable under the measured Gromov-Hausdorff convergence. The first class of spaces we consider is...
Orthogonal Basis and Motion in Finsler Geometry
Orthogonal Basis and Motion Finsler Geometry Differential Geometry
2011/9/20
Abstract: Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand ...
Mean curvature flow of Lagrangian submanifolds with isolated conical singularities
Lagrangian submanifolds isolated conical singularities Differential Geometry
2011/9/20
Abstract: In this paper we study the short time existence problem for the (generalized) Lagrangian mean curvature flow in (almost) Calabi--Yau manifolds when the initial Lagrangian submanifold has iso...
Techniques of computations of Dolbeault cohomology of solvmanifolds
Dolbeault cohomology solvmanifolds Differential Geometry
2011/9/20
Abstract: We consider semi-direct products $\C^{n}\ltimes_{\phi}N$ of Lie groups with lattices $\Gamma$ such that $N$ are nilpotent Lie groups with left-invariant complex structures. We compute the Do...
Abstract: In this note, we explain that Ross-Thomas' result on the weighted Bergman kernels on orbifolds can be directly deduced from our previous result. This result plays an important role in the co...
Change of Topology in Mean Convex Mean Curvature Flow
Change of Topology Mean Convex Mean Curvature Flow Differential Geometry
2011/9/19
Abstract: Consider the mean curvature flow of an (n+1)-dimensional, compact, mean convex region in Euclidean space (or, if n<7, in a Riemannian manifold). We prove that elements of the m-th homotopy g...
Uniqueness of compact tangent flows in Mean Curvature Flow
compact tangent flows Mean Curvature Flow Differential Geometry
2011/9/19
Abstract: We show, for mean curvature flows in Euclidean space, that if one of the tangent flows at a given spacetime point consists of a closed, multiplicity-one, smoothly embedded self-similar shrin...
Pseudo-Riemannian Weakly Symmetric Manifolds
Pseudo-Riemannian Weakly Symmetric Manifolds Differential Geometry
2011/9/19
Abstract: There is a well developed theory of weakly symmetric Riemannian manifolds. Here it is shown that several results in the Riemannian case are also valid for weakly symmetric pseudo-Riemannian ...
Bach-flat gradient steady Ricci solitons
Bach-flat gradient Ricci solitons Differential Geometry
2011/9/19
Abstract: In this paper we prove that any $n$-dimensional ($n\ge 4$) complete Bach-flat gradient steady Ricci solitons with positive Ricci curvature is isometric to the Bryant soliton. We also show th...