2011/01/27 by Jaime Ripoll, Ripoll, Jaime, Miriam Telichevesky +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.DG
paper · pdf · doi:10.48550/arxiv.1101.5277
We have withdrawn the paper to make some corrections
openalex publication_date 2011/01/27 · arxiv created 2012/02/27 · arxiv updated 2012/02/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is proved the existence of entire solutions of the Laplace's and minimal hypersurface's PDEs on a Hadamard manifold M under certain curvature conditions by investigating the asymptotic Dirichlet's problems for these PDEs. In the harmonic case it is obtained an existence result which assumes the same growth condition on the sectional curvature as of Theorem 1.2 of E. Hsu \citeHsu but that contemplates cases having Ricci curvature with exponential decay. It is also obtained a result which extends and improves Theorem 3.6 of Choi \citeChoi. In the minimal case one obtains an extension and an improvement of Theorem 1 of N. do Esp'ırito-Santo, S. Fornari and J. Ripoll \citeEFR, and partial extensions of Theorem 5.2 of J. A. Gálvez and H. Rosenberg \citeGR by allowing the sectional curvature of M degenerate to 0 at infinity.