Graph curvature and Laplacian operators form a vibrant area of research at the intersection of differential geometry and graph theory. The concept of graph curvature, inspired by classical Ricci ...

In this paper, we consider the existence of weak solutions for some nonlinear elliptic problems with perturbed gradient under homogeneous Dirichlet boundary conditions. We apply the Galerkin ...

In this article we derive Hamilton type gradient estimate and Souplet-Zhang type gradient estimate for a generalized weighted parabolic heat equation with potential on a weighted Riemannian manifold ...