Minimal surfaces in the three-sphere by desingularizing intersecting Clifford tori

Autor: Nikolaos Kapouleas, David Wiygul

Publikováno v: Mathematische Annalen. 383:119-170

For each integer $$k \ge 2$$ we apply PDE gluing methods to desingularize certain collections of intersecting Clifford tori, thus producing sequences of minimal surfaces embedded in the round three-sphere. The collections of the Clifford tori we use

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::33a45ba1dd483e11985aa921ddcd3612
https://doi.org/10.1007/s00208-021-02169-8

On Affine Minimal Translation Surfaces and Ramanujan Identities

Autor: Mohamd Saleem Lone

Publikováno v: Mediterranean Journal of Mathematics. 18

In this paper, using the Weierstrass–Enneper formula and the hodographic coordinate system, we find the relationships between the Ramanujan identity and a generalized class of minimal translation surfaces, known as affine minimal translation surfac

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::8d14ed439ae38d816d930769d000288a
https://doi.org/10.1007/s00009-021-01849-8

Explicit minimal scherk saddle towers of arbitrary even genera in R3

Autor: A. J. Yucra Hancco, G. A. Lobos, V. Ramos Batista

Publikováno v: Recercat. Dipósit de la Recerca de Catalunya
instname
Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Publicacions Matemàtiques; Vol. 58, Núm. 2 (2014); p. 445-468

Starting from works by Scherk (1835) and by Enneper-Weierstrass (1863), new minimal surfaces with Scherk ends were found only in 1988 by Karcher (see [9, 10]). In the singly periodic case, Karcher's examples of positive genera had been unique until T

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6a7c88e4d9144d8f45d79e8e98f9b9c3
http://hdl.handle.net/2072/403037

Rigidity Theorems of Minimal Surfaces Foliated by Similar Planar Curves

Autor: Daehwan Kim, Juncheol Pyo

Publikováno v: Results in Mathematics. 72:1697-1716

Catenoids, Riemann’s minimal surfaces, and Scherk’s surfaces (doubly periodic minimal surfaces) are classical minimal surfaces in \(\mathbb {R}^3\). The catenoid and Riemann’s minimal surface can be foliated by circles with different radii. Bec

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::fd9b77c293fc3257a0446820199b4036
https://doi.org/10.1007/s00025-017-0754-9

Minimal translation hypersurfaces in E4

Autor: Marilena Moruz, Marian Ioan Munteanu

Publikováno v: Journal of Mathematical Analysis and Applications. 439:798-812

In this paper we consider hypersurfaces in the Euclidean space E 4 defined as the sum of a curve and a surface whose mean curvature vanishes. We call them minimal translation hypersurfaces in E 4 and give a classification of these hypersurfaces.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::04ee79d187ac6b75ca31490a83fcf73d
https://doi.org/10.1016/j.jmaa.2016.02.077