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We prove two-sided estimates of heat kernels on non-parabolic Riemannian manifolds with ends, assuming that the heat kernel on each end separately satisfies the Li-Yau estimate. Résumé. — Nous obte...
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...
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 ...
In this paper we classify n-dimensional Fano manifolds with index >=n-2 and positive second Chern character.
Abstract: We prove that the birational automorphism group of any Calabi-Yau manifold given by a generic hypersurface of multi-degree two in $({\mathbf P^1})^{n+1}$ is isomorphic to the universal Coxet...
Abstract: Let (X,D) be a dlt pair, where X is a normal projective variety. Let S denote the support of the rounddown of D, and K the canonical divisor of X. We show that any smooth family of canonical...
Abstract: We show a relation between the birational superrigidity of Fano manifold and its slope stability in the sense of Ross-Thomas.
Abstract: We show that a Fano manifold (X,-K_X) is not slope stable with respect to a smooth curve Z if and only if (X,Z) is isomorphic to one of (projective space, line), (product of projective line ...
Abstract: We study smooth projective varieties with small dual variety using methods from symplectic topology. We prove the affine parts of such varieties are subcritical, and that the hyperplane clas...

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