Searcharxiv⌕ Search

arXiv subjects

Wei-Dong Ruan

Publications and source records attributed to Wei-Dong Ruan.

At least 19 recordsLinked to original sources
arXiv2020

Yang-Yang functions, Monodromy and knot polynomials

We derive a structure of $\mathbb{Z}[t,t^{-1}]$-module bundle from a family of Yang-Yang functions. For the fundamental representation of the complex simple Lie algebra of classical type, we give explicit wall-crossing formula and prove that the monodromy representation of the $\mathbb{Z}[t,t^{-1}]$-module bundle is equivalent to the braid group representation induced by the universal R-matrices of $U_{h}(g)$. We show that two transformations induced on the fiber by the symmetry breaking deformation and respectively the rotation of two complex parameters commute with each other.

math-ph↗
arXiv2009

Convergence of Calabi-Yau manifolds

In this paper, we study the convergence of Calabi-Yau manifolds under Kähler degeneration to orbifold singularities and complex degeneration to canonical singularities (including the conifold singularities), and the collapsing of a family of Calabi-Yau manifolds.

math.DG↗
arXiv2008

Bounding sectional curvature along a Kähler-Ricci flow

If a normalized Kähler-Ricci flow $g(t),t\in[0,\infty),$ on a compact Kähler $n$-manifold, $n\geq 3$, of positive first Chern class satisfies $g(t)\in 2πc_{1}(M)$ and has $L^{n}$ curvature operator uniformly bounded, then the curvature operator will also uniformly bounded along the flow. Consequently the flow will converge along a subsequence to a Kähler-Ricci soliton.

math.DG↗
arXiv2006

The Fukaya category of symplectic neighborhood of a non-Hausdorff manifold

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.

math.SG↗
arXiv2005

Newton polygon and string diagram

In this work, we discuss graph like image of curves under moment maps and their relation with the Newton polygon of the curve, which has applications to Lagrangian torus fibration of Calabi-Yau manifolds.

math.DG↗
arXiv2004

Degeneration of Kähler-Einstein Manifolds II: The Toroidal Case

In this paper we prove that the Kähler-Einstein metrics for a toroidal canonical degeneration family of Kähler manifolds with ample canonical bundles Gromov-Hausdorff converge to the complete Kähler-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.

math.DG↗
arXiv2003

Generalized special Lagrangian torus fibration for Calabi-Yau hypersurfaces in toric varieties I

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 $X_0$.

math.DG↗
arXiv2003

Degeneration of Kähler-Einstein Manifolds I: The Normal Crossing Case

In this paper we prove that the Kähler-Einstein metrics for a degeneration family of Kähler manifolds with ample canonical bundles Gromov-Hausdorff converge to the complete Kähler-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.

math.DG↗
arXiv2001

Lagrangian Torus Fibrations and Mirror Symmetry of Calabi-Yau Manifolds

In this paper we summarize our recent work in the construction of Lagrangian torus fibrations for Calabi-Yau hypersurfaces in toric varieties and the symplectic Strominger-Yau-Zaslow conjecture, together with some new development. It is submittded to the Proceedings of the Conference in Symplectic Geometry and Mirror Symmetry held in KIAS, Seoul, Korea. The paper was finished in Jan. 2001, with revisions and added reference.

math.DG↗