Bi-Halfspace and Convex Hull Theorems for Translating Solitons

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Bi-Halfspace and Convex Hull Theorems for Translating Solitons. / Chini, Francesco; Møller, Niels Martin.

I: International Mathematics Research Notices, Bind 2021, Nr. 17, 2021, s. 13011–13045.

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Chini, F & Møller, NM 2021, 'Bi-Halfspace and Convex Hull Theorems for Translating Solitons', International Mathematics Research Notices, bind 2021, nr. 17, s. 13011–13045. https://doi.org/10.1093/imrn/rnz183

APA

Chini, F., & Møller, N. M. (2021). Bi-Halfspace and Convex Hull Theorems for Translating Solitons. International Mathematics Research Notices, 2021(17), 13011–13045. https://doi.org/10.1093/imrn/rnz183

Vancouver

Chini F, Møller NM. Bi-Halfspace and Convex Hull Theorems for Translating Solitons. International Mathematics Research Notices. 2021;2021(17):13011–13045. https://doi.org/10.1093/imrn/rnz183

Author

Chini, Francesco ; Møller, Niels Martin. / Bi-Halfspace and Convex Hull Theorems for Translating Solitons. I: International Mathematics Research Notices. 2021 ; Bind 2021, Nr. 17. s. 13011–13045.

Bibtex

@article{3c81d9c934bb4f98b44a8e3a52a901e0,
title = "Bi-Halfspace and Convex Hull Theorems for Translating Solitons",
abstract = "While it is well known from examples that no interesting “halfspace theorem” holds for properly immersed n-dimensional self-translating mean curvature flow solitons in Euclidean space Rn+1⁠, we show that they must all obey a general “bi-halfspace theorem” (aka “wedge theorem”): two transverse vertical halfspaces can never contain the same such hypersurface. The same holds for any infinite end. The proofs avoid the typical methods of nonlinear barrier construction for the approach via distance functions and the Omori–Yau maximum principle. As an application we classify the closed convex hulls of all properly immersed (possibly with compact boundary) n-dimensional mean curvature flow self-translating solitons Σn in Rn+1 up to an orthogonal projection in the direction of translation. This list is short, coinciding with the one given by Hoffman–Meeks in 1989 for minimal submanifolds: all of Rn⁠, halfspaces, slabs, hyperplanes, and convex compacts in Rn⁠.",
author = "Francesco Chini and M{\o}ller, {Niels Martin}",
year = "2021",
doi = "10.1093/imrn/rnz183",
language = "English",
volume = "2021",
pages = "13011–13045",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",
number = "17",

}

RIS

TY - JOUR

T1 - Bi-Halfspace and Convex Hull Theorems for Translating Solitons

AU - Chini, Francesco

AU - Møller, Niels Martin

PY - 2021

Y1 - 2021

N2 - While it is well known from examples that no interesting “halfspace theorem” holds for properly immersed n-dimensional self-translating mean curvature flow solitons in Euclidean space Rn+1⁠, we show that they must all obey a general “bi-halfspace theorem” (aka “wedge theorem”): two transverse vertical halfspaces can never contain the same such hypersurface. The same holds for any infinite end. The proofs avoid the typical methods of nonlinear barrier construction for the approach via distance functions and the Omori–Yau maximum principle. As an application we classify the closed convex hulls of all properly immersed (possibly with compact boundary) n-dimensional mean curvature flow self-translating solitons Σn in Rn+1 up to an orthogonal projection in the direction of translation. This list is short, coinciding with the one given by Hoffman–Meeks in 1989 for minimal submanifolds: all of Rn⁠, halfspaces, slabs, hyperplanes, and convex compacts in Rn⁠.

AB - While it is well known from examples that no interesting “halfspace theorem” holds for properly immersed n-dimensional self-translating mean curvature flow solitons in Euclidean space Rn+1⁠, we show that they must all obey a general “bi-halfspace theorem” (aka “wedge theorem”): two transverse vertical halfspaces can never contain the same such hypersurface. The same holds for any infinite end. The proofs avoid the typical methods of nonlinear barrier construction for the approach via distance functions and the Omori–Yau maximum principle. As an application we classify the closed convex hulls of all properly immersed (possibly with compact boundary) n-dimensional mean curvature flow self-translating solitons Σn in Rn+1 up to an orthogonal projection in the direction of translation. This list is short, coinciding with the one given by Hoffman–Meeks in 1989 for minimal submanifolds: all of Rn⁠, halfspaces, slabs, hyperplanes, and convex compacts in Rn⁠.

U2 - 10.1093/imrn/rnz183

DO - 10.1093/imrn/rnz183

M3 - Journal article

VL - 2021

SP - 13011

EP - 13045

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 17

ER -

ID: 237998348