Finite entropy translating solitons in slabs

Publikation: Working paper › Preprint › Forskning

Standard

Finite entropy translating solitons in slabs. / Souza Gama, Eddygledson; Martín, Francisco; Møller, Niels Martin.

arXiv preprint, 2022.

Publikation: Working paper › Preprint › Forskning

Harvard

Souza Gama, E, Martín, F & Møller, NM 2022 'Finite entropy translating solitons in slabs' arXiv preprint. <https://arxiv.org/abs/2209.01640>

APA

Souza Gama, E., Martín, F., & Møller, N. M. (2022). Finite entropy translating solitons in slabs. arXiv preprint. https://arxiv.org/abs/2209.01640

Vancouver

Souza Gama E, Martín F, Møller NM. Finite entropy translating solitons in slabs. arXiv preprint. 2022.

Author

Souza Gama, Eddygledson ; Martín, Francisco ; Møller, Niels Martin. / Finite entropy translating solitons in slabs. arXiv preprint, 2022.

Bibtex

@techreport{e041790aeedf4f5895e1c4c7bace351c,
title = "Finite entropy translating solitons in slabs",
abstract = "We study translating solitons for the mean curvature flow, Σ2⊆R3 which are contained in slabs, and are of finite genus and finite entropy. As a first consequence of our results, we can enumerate connected components of slices to define asymptotic invariants ω±(Σ)∈N, which count the numbers of {"}wings''. Analyzing these, we give a method for computing the entropies λ(Σ) via a simple formula involving the wing numbers, which in particular shows that for this class of solitons the entropy is quantized into integer steps. Finally, combining the concept of wing numbers with Morse theory for minimal surfaces, we prove the uniqueness theorem that if Σ is a complete embedded simply connected translating soliton contained in a slab with entropy λ(Σ)=3 and containing a vertical line, then Σ is one of the translating pitchforks of Hoffman-Mart{\'i}n-White",
author = "{Souza Gama}, Eddygledson and Francisco Mart{\'i}n and M{\o}ller, {Niels Martin}",
year = "2022",
language = "English",
publisher = "arXiv preprint",
type = "WorkingPaper",
institution = "arXiv preprint",

}

RIS

TY - UNPB

T1 - Finite entropy translating solitons in slabs

AU - Souza Gama, Eddygledson

AU - Martín, Francisco

AU - Møller, Niels Martin

PY - 2022

Y1 - 2022

N2 - We study translating solitons for the mean curvature flow, Σ2⊆R3 which are contained in slabs, and are of finite genus and finite entropy. As a first consequence of our results, we can enumerate connected components of slices to define asymptotic invariants ω±(Σ)∈N, which count the numbers of "wings''. Analyzing these, we give a method for computing the entropies λ(Σ) via a simple formula involving the wing numbers, which in particular shows that for this class of solitons the entropy is quantized into integer steps. Finally, combining the concept of wing numbers with Morse theory for minimal surfaces, we prove the uniqueness theorem that if Σ is a complete embedded simply connected translating soliton contained in a slab with entropy λ(Σ)=3 and containing a vertical line, then Σ is one of the translating pitchforks of Hoffman-Martín-White

AB - We study translating solitons for the mean curvature flow, Σ2⊆R3 which are contained in slabs, and are of finite genus and finite entropy. As a first consequence of our results, we can enumerate connected components of slices to define asymptotic invariants ω±(Σ)∈N, which count the numbers of "wings''. Analyzing these, we give a method for computing the entropies λ(Σ) via a simple formula involving the wing numbers, which in particular shows that for this class of solitons the entropy is quantized into integer steps. Finally, combining the concept of wing numbers with Morse theory for minimal surfaces, we prove the uniqueness theorem that if Σ is a complete embedded simply connected translating soliton contained in a slab with entropy λ(Σ)=3 and containing a vertical line, then Σ is one of the translating pitchforks of Hoffman-Martín-White

M3 - Preprint

BT - Finite entropy translating solitons in slabs

PB - arXiv preprint

ER -

ID: 320122154