The main result of this article states that the (K, N)-cone over some metric measure space
satisfies the reduced Riemannian curvature-dimension condition RCD⁎(KN, N+ 1) if and …

We study the uniqueness of self-adjoint and Markovian extensions of the Laplacian on
weighted graphs. We first show that, for locally finite graphs and a certain family of metrics …

The paper focuses on the L p-Positivity Preservation property (L p-PP for short) on a
Riemannian manifold (M, g). It states that any L p function u with 1< p<+∞, which solves …

We study symmetric diffusion operators on metric measure spaces. Our main question is
whether essential self-adjointness or L p-uniqueness are preserved under the removal of a …

We study the evolution of the heat and of a free quantum particle (described by the
Schrödinger equation) on two-dimensional manifolds endowed with the degenerate …

We investigate the relationship between one of the classical notions of boundaries for
infinite graphs, graph ends, and self‐adjoint extensions of the minimal Kirchhoff Laplacian …

The main focus in this memoir is on Laplacians on both weighted graphs and weighted
metric graphs. Let us emphasize that we consider infinite locally finite graphs and do not …

In this thesis we study energy forms. These are quadratic forms on the space of real-valued
measurable $ m $-ae determined functions $$ E: L^ 0 (m)\to [0,\infty], $$ which assign to a …

This paper deals with symmetry phenomena for solutions to the Dirichlet problem involving
semilinear PDEs on Riemannian domains. We shall present a rather general framework …

The necessity of a Maximum Principle arises naturally when one is interested in the study of
qualitative properties of solutions to partial differential equations. In general, to ensure the …