91 research outputs found
Estimates for the energy density of critical points of a class of conformally invariant variational problems
We show that the energy density of critical points of a class of conformally
invariant variational problems with small energy on the unit 2-disk B_1 lies in
the local Hardy space h^1(B_1). As a corollary we obtain a new proof of the
energy convexity and uniqueness result for weakly harmonic maps with small
energy on B_1.Comment: 17 page
Quantitative rigidity results for conformal immersions
In this paper we prove several quantitative rigidity results for conformal
immersions of surfaces in with bounded total curvature. We show
that (branched) conformal immersions which are close in energy to either a
round sphere, a conformal Clifford torus, an inverted catenoid, an inverted
Enneper's minimal surface or an inverted Chen's minimal graph must be close to
these surfaces in the -norm. Moreover, we apply these results to prove
a corresponding rigidity result for complete, connected and non-compact
surfaces.Comment: 27 pages, to appear in Amer. J. Mat
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