Mathematics Research

My research interests are in differential geometry and partial differential equations arise from geometry and physics.

• Curvature flows on hypersurfaces (submanifolds) of Riemannian manifolds
• Ricci flow 
• Prescribed curvature problems
• Conformal geometry

List of my recent publications

• The Yamabe problem for higher order curvatures, (with Neil Trudinger and Xu-Jia Wang), JDG, Vol. 77(2007), no. 3, 515-553.

• A class of fully nonlinear equations arising from conformal geometry, (with Yan Zhang), Math. Z., Vol. 255, (2007), No. 1, 17-34. 

• Enclosed convex hypersurfaces with maximal affine area, (with Neil Trudinger and Xu-Jia Wang),  Math. Z., 252(2006), no. 3, 497-510.

• Deforming metrics with negative curvature by a fully nonlinear flow,(with Jiayu Li), Calc.Var.PDE., 23(2005), no.1, 33-50.

• Interior curvature bounds for a class of curvature equations,(with J. Urbas and Xu-Jia Wang), Duke Math. J., 123(2004), no.2, 235-264.

• Convex hypersurface of prescribed Weingarten curvatures,(with Neil Trudinger and Xu-Jia Wang), Comm. in Analysis and Geometry, 12(2004), 213-232.

• On the affine diameter of closed convex hypersurfaces, (with Neil S. Trudinger), Bull. Australian Math. Soc., 68(2003), 431-437.

• Geometry of complete hypersurfaces evolved by mean curvature flow, Chin. Ann. of Math., 24(B)(2003), 123-132.

Curriculum Vitae

Copyright © 2004-2008 Weimin Sheng
Last update: Oct 7, 2007