Spacelike minimal surfaces which are graphs in R-1(4)

Autor(es)

Dussan, M. P. ; Franco Filho, A. P. ; Santos, R. S.

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 519, n. 2, p. 23-pg., 2023-03-15.

Resumo

In this work we study a system of two second order nonlinear partial differential equations corresponding to the equations of minimal spacelike graphs in the four-dimensional Minkownski space R-1(4). We obtain a set of entire solutions of these equations, adapting the method of Karl Kommerell used for the analogous problem in R-4. In our technique we replace "graphs of holomorphic functions" by "graphs of generalized harmonic curves" and then we obtain a class of minimal spacelike surfaces in R-1(4) which are also entire graphs with non-zero Gauss curvature. We then provide two versions of the Bernstein Theorem corresponding for the two types of graphs which can occur in R-1(4). Several explicit examples are given. (c) 2022 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 16/23746-6 - Técnicas algébricas, topológicas e analíticas em geometria diferencial e análise geométrica
• Beneficiário: Paolo Piccione
• Modalidade de apoio: Auxílio à Pesquisa - Temático