Article
Helicoidal surfaces rotating/translating under the mean curvature flow
Geometriae Dedicata (Impact Factor: 0.47). 06/2011; DOI: 10.1007/s1071101297162
Source: arXiv

Article: On complete embedded translating solitons of the mean curvature flow that are of finite genus
[Show abstract] [Hide abstract]
ABSTRACT: We desingularise the union of $3$ Grim paraboloids along CostaHoffmanMeeks surfaces in order to obtain what we believe to be the first examples in $\Bbb{R}^3$ of complete embedded translating solitons of the mean curvature flow of arbitrary nontrivial genus. This solves a problem posed by Mart\'in, SavasHalilaj and Smoczyk.01/2015;  [Show abstract] [Hide abstract]
ABSTRACT: In the present article we obtain classification results and topological obstructions for the existence of translating solitons of the mean curvature flow.04/2014;  [Show abstract] [Hide abstract]
ABSTRACT: We study some basic problems of translating solitons: the volume growth, generalized maximum principle, Gauss maps and certain functions related to the Gauss maps, finally we carry out pointwise estimates and integral estimates for the squared norm of the second fundamental form. Those estimates give rigidity theorems for translating solitons in the Euclidean space in higher codimension.10/2014;
Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.