| Abstract: |
| This talk studies degenerate nonlinear partial differential equations arising in curvature flows with noncompact graphical initial hypersurfaces. The evolving hypersurface remains graphical and develops infinite height along the boundary of its support, leading naturally to a free boundary formulation.
We establish uniform a priori estimates up to the infinite-height boundary despite the degeneracy of the equation, and analyze the evolution of the support and its free boundary. Geometric quantities preserved under the flow are also examined.
Finally, we discuss cigar-type traveling wave solutions with flat regions to address Hamilton's problem on the existence of such flows. |
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