Parabolicity, Brownian Exit Time and Properness of Solitons of the Direct and Inverse Mean Curvature Flow
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https://doi.org/10.1007/s12220-019-00291-3 |
Metadatos
Título
Parabolicity, Brownian Exit Time and Properness of Solitons of the Direct and Inverse Mean Curvature FlowFecha de publicación
2019-10-05ISSN
1050-6926Cita bibliográfica
Gimeno, V., Palmer, V. Parabolicity, Brownian Exit Time and Properness of Solitons of the Direct and Inverse Mean Curvature Flow. J Geom Anal 31, 579–618 (2021). https://doi.org/10.1007/s12220-019-00291-3Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://link.springer.com/article/10.1007/s12220-019-00291-3#rightslinkVersión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
We study some potential theoretic properties of homothetic solitons n of the MCF
and the IMCF. Using the analysis of the extrinsic distance function defined on these
submanifolds in Rn+m, we observe similarities and ... [+]
We study some potential theoretic properties of homothetic solitons n of the MCF
and the IMCF. Using the analysis of the extrinsic distance function defined on these
submanifolds in Rn+m, we observe similarities and differences in the geometry of
solitons in both flows. In particular, we show that parabolic MCF-solitons n with
n > 2 are self-shrinkers and that parabolic IMCF-solitons of any dimension are
self-expanders. We have studied too the geometric behavior of parabolic MCF and
IMCF-solitons confined in a ball, the behavior of the mean exit time function for the
Brownian motion defined on as well as a classification of properly immersed MCFself-shrinkers with bounded second fundamental form, following the lines of Cao and
Li (Calc Var 46:879–889, 2013). [-]
Publicado en
The Journal of Geometric Analysis (2021) 31:579–618Entidad financiadora
Research Program of University Jaume I | DGI -MINECO Grant (FEDER) | Generalitat Valenciana
Identificador de la entidad financiadora
UJI, MINECO, Generalitat Valenciana
Código del proyecto o subvención
UJI-B2018-35 | MTM2017-84851-C2-2-P | PrometeoII/2014/064.
Derechos de acceso
© Mathematica Josephina, Inc. 2019
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