dc.contributor.advisor Gao, Zhiyong Anderson, John Patrick 2009-06-04T00:36:56Z 2009-06-04T00:36:56Z 1991 https://hdl.handle.net/1911/16413 Let compact n-dimensional Riemannian manifolds $(M,g),\ (\widehat M,\ g)$ a diffeomorphism $u\sb0: M\to \widehat M,$ and a constant $p > n$ be given. Then sufficiently small $L\sp{p}$ bounds on the curvature of $\widehat M$ and on the difference of $g$ and $u\sbsp{0}{\*}\ g$ guarantee that $u\sb0$ can be continuously deformed to a harmonic diffeomorphism. A vector field $v$ is constructed on the space of mappings $u$ which are $L\sp{2,p}$ close to $u\sb0$ by solving the nonlinear elliptic equation $\Delta v + \widehat{Rc}\ v = -\Delta u.$ It is shown that under sufficient conditions on $u\sb0$ and on the curvature $\widehat{Rm}$ of the target, the integral curve $u\sb t$ of this vector field converges to a harmonic diffeomorphism. Since the objects we work with, such as $v$ and its derivatives, live in bundles over $M$, to prove regularity results we must first adapt standard techniques and results of elliptic theory to the bundle case. Among the generalizations we prove are Moser iteration, a Sobolev embedding theorem, and a Calderon-Zygmund inequality. 67 p. application/pdf eng Mathematics Harmonic diffeomorphisms between manifolds with bounded curvature Thesis Text Mathematics Natural Sciences Rice University Doctoral Doctor of Philosophy Anderson, John Patrick. "Harmonic diffeomorphisms between manifolds with bounded curvature." (1991) Diss., Rice University. https://hdl.handle.net/1911/16413.
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