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三亚国际数学论坛：几何与物理中的偏微分方程（Partial Differential Equations in Geometry and Physics）
三亚国际数学论坛 几何与物理中的偏微分方程
2018/1/11
PDEs are among the most powerful tools in both geometry and physics. Fundamental geometric problems like the Poincare ́ conjecture have been solved with PDEs, and the basic field equations of phy...
三亚国际数学论坛：Partial Differential Equations in Geometry and Physics
三亚国际数学论坛 Partial Differential Equations Geometry Physics
2017/11/24
PDEs are among the most powerful tools in both geometry and physics. Fundamental geometric problems like the Poincare ́ conjecture have been solved with PDEs, and the basic field equations of phy...
THE ENUMERATIVE GEOMETRY OF RATIONAL AND ELLIPTIC CURVES IN PROJECTIVE SPACE
ELLIPTIC CURVES PROJECTIVE SPACE
2015/7/14
We study the geometry of moduli spaces of genus 0 and 1 curves in Pn with
speci ed contact with a hyperplane H. We compute intersection numbers on these spaces that
correspond to the number of degre...
On a fully non-linear elliptic PDE in conformal geometry
Fully nonlinear PDE generalized Yamabe problem
2014/4/3
We give an expository survey on the subject of the Yamabe-type problem and applications. With a recent technique in hand, we also present a simplified proof of the result by Chang-Gursky-Yang on...
Universal Hyperbolic Geometry II: A pictorial overview
Universal Hyperbolic Geometry II pictorial overview
2011/1/18
This article provides a simple pictorial introduction to universal hyperbolic geometry. We explain how to understand the subject using only elementary projective geometry, augmented by a distinguished...
Local Estimates for Some Elliptic Equations Arising from Conformal Geometry
Local Estimates Elliptic Equations Arising Conformal Geometry
2018/4/19
We present some local gradient and Hessian estimates from C0 estimates for some elliptic equations arising from conformal deformations on the manifolds with totally geodesic boundary, which generalize...