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Search Results: 1 - 10 of 73710 matches for " Wei-Dong Ruan "
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Degeneration of Kahler-Einstein hypersurfaces in complex torus to generalized pair of pants decomposition
Wei-Dong Ruan
Mathematics , 2003,
Abstract: In this paper we show that the convergence of complete Kahler-Einstein hypersurfaces in complex torus in the sense of Cheeger-Gromov will canonically degenerate the underlying manifolds into "pair of pants" decomposition. We also construct minimal Lagrangian tori that represent the vanishing cycles of the degeneration.
Deformation of integral coisotropic submanifolds in symplectic manifolds
Wei-Dong Ruan
Mathematics , 2003,
Abstract: In this paper we prove the unobstructedness of the deformation of integral coisotropic submanifolds in symplectic manifolds, which can be viewed as a natural generalization of results of Weinstein for Lagrangian submanifolds.
The Fukaya category of symplectic neighborhood of a non-Hausdorff manifold
Wei-Dong Ruan
Mathematics , 2006,
Abstract: In this paper, using similar idea as in Fukaya-Oh's work ([9]), we devise a method to compute the Fukaya category of certain exact symplectic manifolds by reducing it to the corresponding Morse category of non-Hausdorff manifold as perturbation of the Lagrangian skeleton of the exact symplectic manifold.
Exponential sums, peak sections, and an alternative version of Donaldson's theorems
Wei-Dong Ruan
Mathematics , 2006,
Abstract: In this paper, we provide an alternative proof of Donaldson's almost-holomorphic section theorem and symplectic Lefschetz pencil theorem, through constructions of certain special kind of Donaldson-type sections of the line bundle based on properties of exponential sums.
Lagrangian torus fibration and mirror symmetry of Calabi-Yau hypersurface in toric variety
Wei-Dong Ruan
Mathematics , 2000,
Abstract: In this paper we give a construction of Lagrangian torus fibration for Calabi-Yau hypersurface in toric variety via the method of gradient flow. Using our construction of Lagrangian torus fibration, we are able to prove the symplectic topological version of SYZ mirror conjecture for generic Calabi-Yau hypersurface in toric variety. We will also be able to give precise formulation of SYZ mirror conjecture in general (including singular locus and duality of singular fibres).
Degeneration of K?hler-Einstein Manifolds I: The Normal Crossing Case
Wei-Dong Ruan
Mathematics , 2003,
Abstract: In this paper we prove that the K\"{a}hler-Einstein metrics for a degeneration family of K\"{a}hler manifolds with ample canonical bundles Gromov-Hausdorff converge to the complete K\"{a}hler-Einstein metric on the smooth part of the central fiber when the central fiber has only normal crossing singularities inside smooth total space. We also prove the incompleteness of the Weil-Peterson metric in this case.
Generalized special Lagrangian torus fibration for Calabi-Yau hypersurfaces in toric varieties I
Wei-Dong Ruan
Mathematics , 2003,
Abstract: In this paper we start the program of constructing generalized special Lagrangian torus fibrations for Calabi-Yau hypersurfaces in toric variety near the large complex limit, with respect to the restriction of a toric metric on the toric variety to the Calabi-Yau hypersurface. The construction is based on the deformation of the standard toric generalized special Lagrangian torus fibration of the large complex limit $X_0$. In this paper, we will deal with the region near the smooth top dimensional torus fibres of $X_0$ and its mirror dual situation: the region near the 0-dimensional fibres of $X_0$.
Generalized special Lagrangian torus fibration for Calabi-Yau hypersurfaces in toric varieties II
Wei-Dong Ruan
Mathematics , 2003,
Abstract: In this paper we construct monodromy representing generalized special Lagrangian torus fibrations for Calabi-Yau hypersurfaces in toric varieties near the large complex limit.
Degeneration of K?hler-Einstein Manifolds II: The Toroidal Case
Wei-Dong Ruan
Mathematics , 2003,
Abstract: In this paper we prove that the K\"{a}hler-Einstein metrics for a toroidal canonical degeneration family of K\"{a}hler manifolds with ample canonical bundles Gromov-Hausdorff converge to the complete K\"{a}hler-Einstein metric on the smooth part of the central fiber when the base locus of the degeneration family is empty. We also prove the incompleteness of the Weil-Peterson metric in this case.
Lagrangian torus fibration of quintic Calabi-Yau hypersurfaces II: Technical results on gradient flow construction
Wei-Dong Ruan
Mathematics , 2004,
Abstract: This paper provides the technical details of gradient flow construction and related problems, which are essential for our construction of Lagrangian torus fibrations for Calabi-Yau hypersurfaces.
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