SeminarsFinite-Time Blow Up for the Heat Flow of Pseudoharmonic Maps
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In our previous work, we proved global existence of the solution for the pseudoharmonic map heat flow from a closed pseudohermitian manifold into a Riemannian manifold with nonpositive sectional curvature. In this talk, we show that the solution of the heat flow of pseudoharmonic maps blows up in finite time if the initial map belongs to some nontrivial homotopy class and its initial energy is sufficiently small. As a consequence, we obtain global existence for the heat flow of pseudoharmonic maps without the curvature assumption on the target manifold.
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Ting-Hui Chang
2013-10-03
11:00:00 - 12:00:00
308 , Mathematics Research Center Building (ori. New Math. Bldg.)
In our previous work, we proved global existence of the solution for the pseudoharmonic map heat flow from a closed pseudohermitian manifold into a Riemannian manifold with nonpositive sectional curvature. In this talk, we show that the solution of the heat flow of pseudoharmonic maps blows up in finite time if the initial map belongs to some nontrivial homotopy class and its initial energy is sufficiently small. As a consequence, we obtain global existence for the heat flow of pseudoharmonic maps without the curvature assumption on the target manifold.