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Autor:
Lerma, Ana M., Manzano, José M.
Publikováno v:
Annali di Matematica Pura ed Applicata, 196 (2017), no. 4, 1345-1364
A Killing submersion is a Riemannian submersion from a 3-manifold to a surface, both connected and orientable, whose fibres are the integral curves of a Killing vector field, not necessarily unitary. The first part of this paper deals with the classi
Externí odkaz:
http://arxiv.org/abs/1604.00542
We describe the evolution under the mean curvature flow of embedded Lagrangian spherical surfaces in the complex Euclidean plane $\mathbb{C}^2$. In particular, we answer the Question 4.7 addressed in [Ne10b] by A. Neves about finding out a condition
Externí odkaz:
http://arxiv.org/abs/1603.03229
Autor:
Castro, Ildefonso, Lerma, Ana M.
Publikováno v:
Results in Maths. 71 (2017), 1109-1125
We study solutions to the inverse mean curvature flow which evolve by homotheties of a given submanifold with arbitrary dimension and codimension. We first show that the closed ones are necessarily spherical minimal immersions and so we reveal the st
Externí odkaz:
http://arxiv.org/abs/1511.03826
Autor:
Castro, Ildefonso, Lerma, Ana M.
Publikováno v:
Journal of Geometry and Physics 75 (2014), 162-172
We introduce a new method to construct a large family of Lagrangian surfaces in complex Euclidean plane by means of two planar curves making use of their usual product as complex functions and integrating the Hermitian product of their position and t
Externí odkaz:
http://arxiv.org/abs/1307.2152
Autor:
Castro, Ildefonso, Lerma, Ana M.
Publikováno v:
International Mathematics Research Notices, 2012, 264, 13 pages
We provide several rigidity results for the Clifford torus in the class of compact self-shrinkers for Lagrangian mean curvature flow.
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/1202.2555
Autor:
Castro, Ildefonso, Lerma, Ana M.
Publikováno v:
Internat. J. Math. 23, No. 10 (2012), 1250101 (16 pages)
Using certain solutions of the curve shortening flow, including self-shrinking and self-expanding curves or spirals, we construct and characterize many new examples of translating solitons for mean curvature flow in complex Euclidean plane. They gene
Externí odkaz:
http://arxiv.org/abs/1007.1886
Autor:
Castro, Ildefonso, Lerma, Ana M.
Publikováno v:
Proc. Amer. Math. Soc. 138 (2010), 1821-1832
We classify all Hamiltonian stationary Lagrangian surfaces in complex Euclidean plane which are self-similar solutions of the mean curvature flow.
Comment: 14 pages
Comment: 14 pages
Externí odkaz:
http://arxiv.org/abs/0906.3117
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 June 2018 462(1):637-647
Publikováno v:
Lenguaje y Textos; 2024, Issue 58, p3-17, 15p