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Regular domains and
surfaces of constant Gaussian curvature in 3-dimensional
affine space
Xin Nie and Andrea Seppi |
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Vol. 15 (2022), No. 3, 643–697
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Abstract |
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Generalizing the notion of domains of dependence in the Minkowski space, we define and study regular domains in the affine space with respect to a proper convex cone. In three dimensions, we show that every proper regular domain is uniquely foliated by some particular surfaces with constant affine Gaussian curvature. The result is based on the analysis of a Monge–Ampère equation with extended real-valued lower semicontinuous boundary condition. |
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Keywords
domain of dependence, affine differential geometry, affine
Gauss–Kronecker curvature, Monge–Ampère equation
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Mathematical Subject Classification 2010
Primary: 53A15
Secondary: 35J96, 53C42
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Milestones
Received: 1 September 2019
Revised: 2 July 2020
Accepted: 13 November 2020
Published: 10 June 2022
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Authors |
| Xin Nie | |
| Shing-Tung Yau Center of Southeast
University Southeast University Nanjing China |
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| Andrea Seppi | |
| CNRS and Université Grenoble
Alpes Gières France |
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