Smooth Local Isometric Embedding of Surfaces with Gauss Curvature Changing Sign Monotonically Across a Curve.
November 02, 2005 02:30 PM to 03:30 PM
Speakers:
Han, Qing
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Abstract: |
In 1986, C.-S. Lin proved the existence of sufficiently smooth local isometric embedding of surfaces with Gauss curvature changing sign cleanly. It is not clear whether such an isometric embedding is smooth if surfaces are smooth. In this talk, we give an affirmative answer to such a question. In general, we prove the existence of smooth local isometric embedding of surfaces with Gauss curvature changing sign monotonically across a curve, where the Gauss curvature may vanish up to finite or infinite order. The proof relies on a careful analysis of linearizations of the Darboux equation and a construction of smooth solutions to a class of degenerate elliptic equations. |
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