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Topic : Homogeneous
Solutions of Elliptic Equations
Speaker :
Professor
Qing Han (University of Notre Dame)
Time
: June
9 (Wednesday) PM 2:00~3:15
Abstract:
In this talk, we shall discuss homogeneous solutions to
non-divergent
linear elliptic equations. We shall prove that any homogeneous degree one
solutions in three dimensional Euclidean space have to be linear. The key step
is to analyze the surface of the gradient map restricted on the unit sphere.
We shall prove that such a surface has at most finitely many singular points
and Gauss curvature is negative away from those points. The topic is
related to an old conjecture by Chern that any minimal 2-sphere in any
$m$-sphere (m>2) is a big circle.
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