International Journal of Nonlinear Analysis and Applications

Semi-Fredholmness on a weighted geometric realization of 2-simplexes and 3- simplexes

Document Type : Research Paper

Authors

1 Laboratoire de Mathematiques Fondamentales et Appliquees, Departement de Mathematiques et Informatique, Faculte des Sciences Ain Chock, Universite Hassan II de Casablanca, Morocco

2 Laboratoire de Mathematiques Fondamentales et Appliquees, Faculte des Sciences Ain Chock, Universite Hassan II de Casablanca, Morocco

Abstract

In this present article, we introduce the notion of oriented $2$-simplexes and the notion of oriented $3$-simplexes and we use them to create a new framework that we call a weighted geometric realization of $2$-simplexes and $3$-simplexes. Next, we define the weighted geometric realization Gauss-Bonnet operator $L$. After that, we present and study the non-parabolicity at the infinity of  $L$. Finally, we develop general conditions to ensure semi-Fredholmness of $L$ based on its non-parabolicity at infinity.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 10
October 2023
Pages 19-34
  • Receive Date: 14 March 2022
  • Revise Date: 19 April 2023
  • Accept Date: 28 May 2023