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CROSS CURVATURE FLOW ON LOCALLY HOMOGENEOUS THREE-MANIFOLDS (II)
CURVATURE FLOW THREE-MANIFOLDS
2015/8/17
In this paper, we study the positive cross curvature flow on locally
homogeneous 3-manifolds. We describe the long time behavior of these flows. We
combine this with earlier results conc...
BACKWARD RICCI FLOW ON LOCALLY HOMOGENEOUS THREE-MANIFOLDS
THREE-MANIFOLDS LOCALLY HOMOGENEOUS
2015/8/17
In this paper, we study the backward Ricci flow on locally homogeneous
3-manifolds. We describe the long time behavior and show that, typically and after
a proper re-scaling, there is converge...
CROSS CURVATURE FLOW ON LOCALLY HOMOGENOUS THREE-MANIFOLDS (I)
HOMOGENOUS THREE-MANIFOLDS CURVATURE FLOW
2015/8/17
Chow and Hamilton introduced the cross curvature flow on closed 3-
manifolds with negative or positive sectional curvature. In this paper, we study
the negative cross curvature flow in t...
CALABI’S EXTREMAL METRICS ON TORIC MANIFOLDS.
Infinite dimensional Morse theory for geodesics on Finsler manifolds
Infinite dimensional Morse theory geodesics Finsler manifolds
2015/3/18
Infinite dimensional Morse theory for geodesics on Finsler manifolds.
Let f:X\rightarrow X be a dominant meromorphic self-map, where X is a compact, connected complex manifold of dimension n > 1. Suppose there is an embedded copy of \mathbb P^1 that is invariant under f...
VOLUME COMPARISON OF CONFORMALLY COMPACT MANIFOLDS WITH SCALAR CURVATURER≥ −n(n−1)
CONFORMALLY COMPACT MANIFOLDS called renormal-ized volume
2014/9/26
In this paper, we present a global invariant, called renormal-ized volume, which can be defined for a large class of conformally compact
manifolds. We use this definition to show a local volume compa...
ON THE RENORMALIZED VOLUMES FOR CONFORMALLY COMPACT EINSTEIN MANIFOLDS
THE RENORMALIZED VOLUMES CONFORMALLY COMPACT EINSTEIN MANIFOLDS
2014/4/3
We study the renormalized volume of a conformally compact Einstein manifold. In even dimenions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the...
ON A CONFORMAL GAP AND FINITENESS THEOREM FOR A CLASS OF FOUR MANIFOLDS
ON A CONFORMAL GAP FINITENESS THEOREM CLASS OF FOUR MANIFOLDS
2014/4/3
In this paper we develop a bubble tree structure for a degenerating class of Riemannian metrics satisfying some global conformal bounds on compact manifolds of dimension 4. Applying the bubble tree st...
ON THE RENORMALIZED VOLUMES FOR CONFORMALLY COMPACT EINSTEIN MANIFOLDS
ON THE RENORMALIZED VOLUMES CONFORMALLY COMPACT EINSTEIN MANIFOLDS
2014/4/3
We study the renormalized volume of a conformally compact Einstein manifold. In even dimenions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the...
On f-bi-harmonic maps between Riemannian manifolds
f-bi-harmonic maps Riemannian manifolds
2018/4/19
Abstract: Both bi-harmonic map and $f$-harmonic map have nice physical motivation and applications. In this paper, by combination of these two harmonic maps, we introduce and study $f$-bi-harmonic map...
HODGE METRIC COMPLETION OF THE TEICHM¨ ULLER SPACE OF CALABI–YAU MANIFOLDS
HODGE METRIC COMPLETION TEICHM¨ ULLER SPACE CALABI–YAU MANIFOLDS
2018/4/19
We prove that the Hodge metric completion of the Teichm¨uller space of polarized and marked Calabi–Yau manifolds is a complex affine manifold. We also show that the extended period map from the comple...
HODGE THEORY AND DEFORMATIONS OF KAHLER MANIFOLDS
HODGE THEORY DEFORMATIONS KAHLER MANIFOLDS
2018/4/19
We prove several formulas related to Hodge theory and the Kodaira-Spencer-Kuranishi deformation theory of K¨ahler manifolds. As applications, we present a construction of globally convergent power ser...
Maximal multipliers on compact manifolds without boundary
Maximal multipliers compact manifolds boundary Analysis of PDEs
2012/7/11
Hormander-Mihklin type multiplier theorem on compacts manifolds withour boundary has been obtained by using the wave kernels. We consider maximal multiplies on this setting. To obtain the result, we c...
GLOBAL TORELLI THEOREM FOR PROJECTIVE MANIFOLDS OF CALABI-YAU TYPE
GLOBAL TORELLI THEOREM PROJECTIVE MANIFOLDS CALABI-YAU TYPE
2018/4/19
In this paper we prove two main results about the global properties of the period mapsfrom the Teichm¨uller space of polarized and marked Calabi-Yau type manifolds to theperiod domain of polarized Hod...