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Remarks on solitons for inverse mean curvature flow
Author(s) -
Kim Daehwan,
Pyo Juncheol
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201900128
Subject(s) - homothetic transformation , mathematics , curvature , soliton , inverse , mean curvature flow , flow (mathematics) , mathematical analysis , translation (biology) , mathematical physics , mean curvature , pure mathematics , geometry , physics , nonlinear system , quantum mechanics , biochemistry , chemistry , messenger rna , gene
Homothetic and translating solitons for the inverse mean curvature flow (IMCF) in R n + 1are self‐similar solutions deformed by only homothety and translation under IMCF, respectively. In this paper, we address some geometric properties of these solitons. To be specific, the incompleteness for the homothetic soliton of velocity C with 0 < C < 1 nand for any translating soliton are proved. In addition, we show that the quantitative area growth for the homothetic solitons for C ≥ 1 nand the translating solitons.