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 -