| Full text | |
| Author(s): |
Dussan, M. P.
;
Franco Filho, A. P.
;
Santos, R. S.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Journal of Mathematical Analysis and Applications; v. 519, n. 2, p. 23-pg., 2023-03-15. |
| Abstract | |
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) | |
| FAPESP's process: | 16/23746-6 - Algebraic, topological and analytical techniques in differential geometry and geometric analysis |
| Grantee: | Paolo Piccione |
| Support Opportunities: | Research Projects - Thematic Grants |