As on arXiv
Abstract
We investigate the evolution of strictly convex hypersurfaces driven by the -Hessian curvature flow, subject to the second boundary condition. We first explore the translating solutions corresponding to this boundary value problem. Next, we establish the long-time existence of the flow and prove that it converges to a translating solution. To overcome the difficulty of driving boundary estimates, we employ an orthogonal invariance technique. Using this method, we extend the results of Schnürer-Smoczyk and Schnürer from the second boundary value problem of Gauss curvature flow to -Hessian curvature flow.
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Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Inverse Hessian Curvature Flow in Minkowski Space II: The Dirichlet problem at infinity
Topics Self-shrinkers & translators, Long-time existence & convergence, Boundaries & non-compact · Same author Zhizhang Wang · Shared terms “Hessian curvature”, “boundary value”, “strictly convex”
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Translating solutions and the entire Hessian curvature flow in Minkowski space
Topics Self-shrinkers & translators, Long-time existence & convergence, Boundaries & non-compact · Shared terms “Hessian curvature”, “translating solution”, “strictly convex”
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On the second boundary value problem for mean curvature flow in Minkowski space
Topics Self-shrinkers & translators · Same author Rongli Huang · Shared terms “boundary value”, “Gauss”
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Inverse Hessian Curvature Flow in Minkowski Space I: Cocompact Hypersurfaces
Topics Long-time existence & convergence, Other curvature flows · Same author Zhizhang Wang · Shared terms “Hessian curvature”
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Entire convex curvature flow in Minkowski space
Topics Self-shrinkers & translators, Long-time existence & convergence, Boundaries & non-compact · Same author Zhizhang Wang
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Entire curvature flow in Minkowski space
Topics Self-shrinkers & translators, Long-time existence & convergence, Boundaries & non-compact · Same author Zhizhang Wang
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Invariant -translators for the Gauss curvature flow in Euclidean space
Topics Gauss curvature flow, Self-shrinkers & translators, Other curvature flows
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Gauss Curvature Flow on Surfaces of Revolution – The Noncompact Case
Topics Gauss curvature flow, Boundaries & non-compact, Other curvature flows · Shared terms “boundary value”
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