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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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...

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