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Energy Growth in Minimal Surface Bubbles John Douglas Moore

Summary: Energy Growth in Minimal Surface Bubbles
John Douglas Moore
Department of Mathematics
University of California
Santa Barbara, CA, USA 93106
e-mail: moore@math.ucsb.edu
November 16, 2007
This article is concerned with conformal harmonic maps f : M
from a closed connected surface into a compact Riemannian manifold M
of dimension at least four, studied via a perturbative approach based upon
the -energy of Sacks and Uhlenbeck. It gives an estimate on the rate
of growth of energy density in the bubbles of minimax -energy critical
points as 1, when the bubbles are at a distance at least L0 > 0 from
the base. It also describes additional techniques hopefully useful for the
development of a partial Morse theory for closed parametrized minimal
surfaces (or harmonic surfaces) in compact Riemannian manifolds.
1 Introduction
The Morse theory of geodesics in Riemannian manifolds is a highly success-
ful application of the techniques of global analysis to calculus of variations for


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics