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The Log-Convex Density Conjecture and vertical surface area in warped products
The Log-Convex Density Conjecture vertical surface area warped products Differential Geometry
2011/9/19
Abstract: We examine the vertical component of surface area in the warped product of a Euclidean interval and a fiber manifold with product density. We determine general conditions under which vertica...
Bounds on volume growth of geodesic balls under Ricci flow
geodesic balls under Ricci flow Differential Geometry Analysis of PDEs
2011/9/16
Abstract: We prove a so called $\kappa$ non-inflating property for Ricci flow, which provides an upper bound for volume ratio of geodesic balls over Euclidean ones, under an upper bound for scalar cur...
Weyl-Schouten Theorem for symmetric spaces
Weyl tensor symmetric space Differential Geometry
2011/9/16
Abstract: Let N be a symmetric space of dimension n > 5 whose de Rham decomposition contains no factors of constant curvature and let W be the Weyl tensor of N at some point. We prove that a Riemannia...
Projectively deformable Legendrian surfaces
Legendrian surface projective deformation del Pezzo surface
2011/9/16
Abstract: Consider an immersed Legendrian surface in the five dimensional complex projective space equipped with the standard homogeneous contact structure. We introduce a class of fourth order projec...
Abstract: We consider here the problem of classifying orbits of an action of the dif- feomorphism group of 3-space on a tower of fibrations with P2-fibers that generalize the Monster Tower due to Mont...
Supremum of Perelman's entropy and Kahler-Ricci flow on a Fano manifold
Kahler-Ricci flow Kahler-Ricci solitons Perelman entropy
2011/9/15
Abstract: In this paper, we extend the method in [TZhu5] to study the energy level $L(\cdot)$ of Perelman's entropy $\lambda(\cdot)$ for K\"ahler-Ricci flow on a Fano manifold. Consequently, we first ...
General perversities and L^2 de Rham and Hodge theorems for stratified pseudomanifolds
Hodge theorems stratified pseudomanifolds Differential Geometry
2011/9/15
Abstract: Given a compact stratified pseudomanifold with a Thom-Mather stratification and a class of riemannian metrics over its regular part, we study the relationships between the $L^{2}$ de Rham an...
Geography of symplectic 4- and 6-manifolds
Symplectic geography symplectic sums symplectic structures
2011/9/15
Abstract: The geography of minimal symplectic 4-manifolds with arbitrary fundamental group and symplectic 6-manifolds with abelian fundamental group of small rank, and with arbitrary fundamental group...
Abstract: In this paper, we construct the index bundle gerbe of a family of self-adjoint Dirac-type operators, refining a construction of Segal. In a special case, we construct a geometric bundle gerb...
Caccioppoli's inequalities on constant mean curvature hypersurfaces in Riemannian manifolds
Caccioppoli’s inequality Simons’ equation constant mean curvature hypersurfaces stable finite index
2011/9/14
Abstract: We prove some Caccioppoli's inequalities for the traceless part of the second fundamental form of a complete, non compact, finite index, constant mean curvature hypersurface of a Riemannian ...
Local Equivalence Problem for Sub-Riemannian Structures
Sub-Riemannian Structures Differential Geometry
2011/9/15
Abstract: We solve the local equivalence problem for sub-Riemannian structures on (2n + 1)-dimensional manifolds. We show that two sub-Riemannian structures are locally equivalent if and only if? thei...
Some Singular Limit Laminations of Embedded Minimal Planar Domains
Singular Limit Laminations Embedded Minimal Planar Domains Differential Geometry
2011/9/15
Abstract: In this paper we give two examples of sequences of embedded minimal planar domains in $\mathbb{R}^3$ which converge to singular laminations of $\mathbb{R}^3$. In contrast with the situation ...
A note on compact gradient Yamabe solitons
compact gradient Yamabe soliton Yamabe flow constant scalar curvature metric
2011/9/15
Abstract: We will give a simple proof that the metric of any compact Yamabe gradient soliton (M,g) is a metric of constant scalar curvature when the dimension of the manifold n>2.
Generalized Ricci flow I: Local existence and uniqueness
Generalized Ricci flow uniformly parabolic system short-time existence Thurston’s eight geometries
2011/9/13
Abstract: In this paper we investigate a kind of generalized Ricci flow which possesses a gradient form. We study the monotonicity of the given function under the generalized Ricci flow and prove that...
A mass-decreasing flow in dimension three
mass-decreasing flow dimension three Differential Geometry
2011/9/13
Abstract: In this article, we introduce a mass-decreasing flow for asymptotically flat three-manifolds with nonnegative scalar curvature. This flow is defined by iterating a suitable Ricci flow with s...