The equation of prescribed gauss curvature without boundary conditions

Urbas, John I.E.

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The equation of prescribed gauss curvature without boundary conditions

Date

1984

Authors

Urbas, John I.E.

Abstract

A necessary condition for the equation of prescribed Gauss curvature to have a convex solution defined on a domain Ω ⊂ Rn is that the Gauss curvature K satisfies ∫Ω K ≤ ωn. We prove the existence, uniqueness and regularity, under suitable hypotheses, of a convex solution in the extremal case ∫Ω K = ωn. We also discuss the boundedness of convex solutions of the equation.

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https://dspace-test.anu.edu.au/handle/1885/733743937

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DevOps Pure Testing

Source

Journal of Differential Geometry

Type

Article

DOI

10.4310/jdg/1214439282

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The equation of prescribed gauss curvature without boundary conditions

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