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In this paper, we study the gradient estimates of Hamilton type for positive solutions to both drifting heat equation and the simple nonlinear heat equation problem ut − u = au log u, u > 0 on ...
Round handles are aliated with smooth 4-manifolds in two major ways: 5-dimensional round handles appear extensively as the building blocks in cobordisms between 4-manifolds, whereas 4-dimensional rou...
We prove heat kernel estimates for the ¯@-Neumann Laplacian  acting in spaces of differential forms over noncompact manifolds with a Lie group symmetry and compact quotient. We also relate our ...
Mixed 3-structures are odd-dimensional analogues of paraquaternionic structures. They appear naturally on lightlike hypersurfaces of almost paraquaternionic hermitian manifolds. We study invariant and...
We extract an invariant taking values in N ∪ {∞}, which we call the order of algebraic torsion, from the Symplectic Field Theory of a closed contact manifold, and show that its finiteness gives obstru...
This work develops the recent proposition to use dimensional reduction from the four-imensional space-time to the one with a smaller number of dimensions (1 + d); d < 3 at high enough energy.To this g...
Let   Rn be an n-dimensional integral Delzant polytope. It is wellknown that there exist the n-dimensional compact toric manifold X and the very ample (C×)n-equivariant line bundle L on X associa...
In our previous works on deformation limits of projective and Moishezon manifolds, we introduced and made crucial use of the notion of strongly Gauduchon metrics as a reinforcement of the earlier noti...
We present a general framework for reduction of symplectic Qmanifolds via graded group actions. In this framework, the homological structure on the acting group is a multiplicative multivector field.
In joint work with Chen and Weber [7] , the author has elsewhere shown that CP2#2CP2 admits an Einstein metric. The present paper gives a new and rather different proof of this fact. Our results inclu...
We study smooth complex projective polarized varieties (X;H)of dimension n  2 which admit a dominating family V of rational curves of H-degree 3, such that two general points of X may be joined by a ...
Pinching on open manifolds      Pinching  open manifolds        2010/12/7
We show that the 2-jet bundle of local Riemannian metrics on an arbitrary differentiable manifold admits a section which pointwise fulfills the curvature relation sec(g) = a for any a 2 R. It follows ...
Extrinsic Geometric Flows (EGF) for a codimension-one foliation have been recently introduced by authors as deformations of Riemannian metrics subject to quantities expressed in terms of its second fu...
We show the T2-cobordism group of the category of 4-dimensional quasitoric manifolds is generated by the T2-cobordism class of CP2. The main tool is the theory of quasitoric manifolds.
This paper contains several results concerning circle action on almost-complexand smooth manifolds. More precisely, we show that, for an almost-complex manifoldM2mn(resp. a smooth manifold N4mn), if t...

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