University of California, Irvine

Department of Mathematics

Differential Geometry Seminar

Spring 2003, MSTB 254, Tuesdays 4-5pm

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Date Time & Location Speaker
Title
TUESDAY
(Apr. 15) 		4:00PM
in MSTB 254 		Weidong Ruan
(UIC)		 Degeneration of Kahler-Einstein manifolds
THURSDAY
(Apr 17) 		3:00PM
in MSTB 256		 Mu-Tao Wang
(Columbia)		 Mean curvature flows and homotopy of maps between spheres
TUESDAY
(Apr. 29) 		4:00PM
in MSTB 254 		Elton Hsu
(Northwestern) 		Heat semigroup dominations for manifolds with boundary
TUESDAY
(May 6) 		4:00PM
in MSTB 254 		Yu Yuan
(U. Washington)		 Homogeneous solutions to elliptic equations
TUESDAY
(May 13) 		4:00PM
in MSTB 254 		Jaigyoung Choe
(Seoul U & Stanford U)		 Relative isoperimetric inequality: an optimal extension of the classical isoperimetric inequality
TUESDAY
(May 27) 		4:00PM
in MSTB 254 		Naichung Leung
(Minnesota & IPAM)		 Instantons and Lagrangians on manifolds with
vector cross product
Wednesday
(Jul 23) 		3:00PM
in MSTB 107		 Lei Ni
(UCSD)		 Structure theorems on nonnegativiely curved complete Kaehler manifolds

May 6, Yu Yuan

We classify homogeneous order d solutions to (fully nonlinear) elliptic equations in dimension three, and in higher dimensions except d=2. A special case is the well-known result that any nonparametric minimal cone of dimension three must be flat. This is joint work with Nadirashvili, and with Han, Nadirashvili for d=2 in dimension three.

May 15, Jaigyoung Choe

It is well known that a domain D in R^n satisfies the classical isoperimetric inequality (CII) and that equality holds in CII if and only if D is a ball. It has been conjectured that CII should hold for any compact minimal submanifold M^n in R^m. This conjecture is known to be
true only for M^2 with one or two boundary components and for any area minimizing M^n. Also it has been conjectured that every domain D in a simply connected nonpositively curved Riemannian manifold M^n should satisfy CII. So far this is proved for n=2,3, and 4 only. In this talk we consider another optimal extension of CII called the relative isoperimetric inequality: Given a domain D in the exterior of a convex domain C in R^n or in a simply connected nonpositively curved M^n, show that D satisfies half the CII with equality if and only if D is a half ball and C is a half space.