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Growth of Energy in Minimal Surface Bubbles John Douglas Moore

Summary: Growth of Energy in Minimal Surface Bubbles
John Douglas Moore
Department of Mathematics
University of California
Santa Barbara, CA, USA 93106
e-mail: moore@math.ucsb.edu
Preliminary version
This article is concerned with developing tools for investigating har-
monic maps f : M from a closed Riemann surface into a compact
manifold M of dimension at least three, using a perturbative approach
based upon the -energy of Sacks and Uhlenbeck. We present a replace-
ment procedure for -harmonic maps which is similar to one that has
been used for harmonic maps, and show how it can be used to investigate
the structure of critical points for the -energy, when > 1 is sufficiently
close to one. We give an estimate on the rate of growth of the energy
density in the bubbles of such critical points as 1, when the bubbles
are at a distance at least L0 > 0 from the base.
1 Prologue
The Morse theory of geodesics is a highly successful application of global analysis


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


Collections: Mathematics