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Translating solutions
to the Gauss curvature flow with flat sides
Kyeongsu Choi, Panagiota Daskalopoulos and Ki-Ahm Lee |
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Vol. 14 (2021), No. 2, 595–616
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Abstract |
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We derive local estimates for complete noncompact translating solitons of the Gauss curvature flow in which are graphs over a convex domain . This is closely is related to deriving local estimates for the degenerate Monge–Ampère equation. As a result, given a weakly convex bounded domain , we establish the existence of a translating soliton. In particular, when the boundary has line segments, we show the existence of flat sides of the translator from a local a priori nondegeneracy estimate near the free boundary. |
Keywords
Gauss curvature flow, translator, regularity, free boundary
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Mathematical Subject Classification 2010
Primary: 53C44
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Milestones
Received: 20 November 2018
Revised: 9 September 2019
Accepted: 25 October 2019
Published: 20 March 2021
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Authors |
| Kyeongsu Choi | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States |
Korea Institute for Advanced
Study Seoul South Korea |
| Panagiota Daskalopoulos | |
| Department of Mathematics Columbia University New York, NY United States |
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| Ki-Ahm Lee | |
| Department of Mathematical
Sciences Seoul National University Seoul South Korea |
Korea Institute for Advanced
Study Seoul South Korea |
