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MEAN CURVATURE FLOW OF HIGHER CODIMENSION IN RIEMANNIAN MANIFOLDS
MEAN CURVATURE HIGHER CODIMENSION RIEMANNIAN MANIFOLDS
2018/4/19
We investigate the convergence of the mean curvature flow of arbitrary codimension in Riemannian manifolds with bounded geometry. We prove that if the initial submanifold satisfies a pinching conditio...
A GLOBAL TORELLI THEOREM FOR CALABI-YAU MANIFOLDS
A GLOBAL TORELLI THEOREM CALABI-YAU MANIFOLDS
2018/4/19
We prove that the period map from the Teichm¨uller space of polarized and marked Calabi-Yau manifolds to the classifying space of polarized Hodge structures is an embedding. The proof is based on the ...
ON THE INJECTIVITY RADIUS GROWTH OF COMPLETE NONCOMPACT RIEMANNNIAN MANIFOLDS
INJECTIVITY RADIUS GROWTH COMPLETE NONCOMPACT RIEMANNNIAN MANIFOLDS
2018/4/19
In this paper we introduce a global geometric invariant (M) related to injectivityradius to complete non-compact Riemannian manifolds and prove: If (Mn) > 1,then Mn is isometric to Rn when Ricci curva...
Invariant tensors related with natural connections for a class Riemannian product manifolds
Invariant tensors natural connections class Riemannian product manifolds Differential Geometry
2012/6/29
Some invariant tensors in two Naveira classes of Riemannian product manifolds are considered. These tensors are related with natural connections, i.e. linear connections preserving the Riemannian metr...
Automorphism groups of Calabi-Yau manifolds of Picard number two
Automorphism groups Calabi-Yau manifolds Picard number two Algebraic Geometry
2012/6/29
We prove that the automorphism group of an odd dimensional Calabi-Yau manifold of Picard number two is always a finite group. This makes a sharp contrast to the automorphism groups of K3 surfaces and ...
Biharmonic Semi-Riemannian Submersions from 3-manifolds
Semi-Riemannian submersions 3-manifolds Differential Geometry
2012/6/30
The main interest of the present paper is to prove the dual results for semi-Riemannian submersions, i.e., a semi-Riemannian submersion from a 3-dimensional space form into a surface is biharmonic if ...
Notes on the peripheral volume of hyperbolic 3-manifolds
Notes the peripheral volume hyperbolic 3-manifolds Geometric Topology
2012/6/27
We consider hyperbolic 3-manifolds with either non-empty compact geodesic boundary, or some toric cusps, or both. For any such M we analyze what portion of the volume of M can be recovered by insertin...
Convergence of scalar-flat metrics on manifolds with boundary under the Yamabe flow
Convergence of scalar-flat metrics manifolds boundary under the Yamabe flow Differential Geometry
2012/6/21
This paper is concerned with a Yamabe-type flow for compact Riemannian manifolds with boundary. The convergence of this flow is established if the manifold with boundary satisfies either a generic con...
On the classification of homogeneous Einstein metrics on generalized flag manifolds with $b_2(M)=1$
Homogeneous Einstein metric flag manifold second Betti number finiteness conjecture twistor fibration
2012/6/25
We study homogeneous Einstein metrics for a class of compact homogeneous spaces, namely generalized flag manifolds $G/H$ with second Betti number $b_{2}(G/H)=1$. There are 33 such manifolds which have...
Classification of 2-Fano manifolds with high index
Classification of 2-Fano manifolds high index Algebraic Geometry
2012/6/27
In this paper we classify n-dimensional Fano manifolds with index >=n-2 and positive second Chern character.
The Yamabe constant on noncompact manifolds
The Yamabe constant noncompact manifolds Differential Geometry
2012/6/19
We prove several facts about the Yamabe constant of Riemannian metrics on general noncompact manifolds and about S. Kim's closely related "Yamabe constant at infinity". In particular we show that the ...
Thomas Bayes' walk on manifolds
Bayesian nonparametrics Gaussian process priors Heat kernel
2012/6/19
Convergence of the Bayes posterior measure is considered in canonical statistical settings where observations sit on a geometrical object such as a compact manifold, or more generally on a compact met...
Symplectic 4-manifolds with fixed point free circle actions
Symplectic 4-manifolds point free circle actions Geometric Topology
2012/6/19
We show that recent results of Friedl-Vidussi and Chen imply that a symplectic manifold admits a fixed point free circle action if and only if it admits a symplectic circle action and we give a comple...
Nonpositively curved manifolds containing a prescribed nonpositively curved hypersurface
Nonpositively curved manifolds prescribed nonpositively curved hypersurface Differential Geometry
2012/6/9
We use pinched smooth hyperbolization to show that every closed, nonpositively curved $n$-dimensional manifold $M$ can be embedded as a totally geodesic submanifold of a closed, nonpositively curved $...
Analytic torsion versus Reidemeister torsion on hyperbolic 3-manifolds with cusps
Analytic torsion Reidemeister torsion hyperbolic 3-manifolds cusps Spectral Theory
2012/6/14
For a non-compact hyperbolic 3-manifold with cusps we prove an explicit formula that relates the regularized analytic torsion associated to the even symmetric powers of the standard representation of ...