Regularity of minimal submanifolds and mean curvature flows meeting along a common free boundary

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• Brian Krummel (UT, Austin)
• Monday 31 October 2016, 15:00-16:00
• CMS, MR13.

If you have a question about this talk, please contact Prof. Neshan Wickramasekera.

We consider the higher regularity of a minimal submanifold $M$ in a Riemannian manifold $N$ such that $M$ is the union of submanifolds-with-boundary $M_1,…,M_q$ meeting along a common boundary $\Gamma$.  When $N$ is smooth (real-analytic), we show that $M_1,…,M_q$ and $\Gamma$ are smooth (real-analytic) submanifolds.  This result was previously proven by Kindlerher, Nirenberg, and Spruck in the special case $q = 3$ and codimension one using a partial holograph transformation.  We extend their result to all $q \geq 3$ and all codimensions.  We then apply the result to the work of Wickramasekera and Hughes on minimal submanifolds and joint work of Schultz and White on network flows.

This talk is part of the Partial Differential Equations seminar series.

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