Sharp borderline Sobolev inequalities on compact Riemannian manifolds.
Solutions of DEs and PDEs as potential maps using first order Lagrangians.
Some non-linear function theoretic properties of Riemannian manifolds.
We study the appropriate versions of parabolicity stochastic completeness and related Liouville properties for a general class of operators which include the p-Laplace operator, and the non linear singular operators in non-diagonal form considered by J. Serrin and collaborators.
Stability results for Harnack inequalities
We develop new techniques for proving uniform elliptic and parabolic Harnack inequalities on weighted Riemannian manifolds. In particular, we prove the stability of the Harnack inequalities under certain non-uniform changes of the weight. We also prove necessary and sufficient conditions for the Harnack inequalities to hold on complete non-compact manifolds having non-negative Ricci curvature outside a compact set and a finite first Betti number or just having asymptotically...
Subharmonic functions in sub-Riemannian settings
In this paper we furnish mean value characterizations for subharmonic functions related to linear second order partial differential operators with nonnegative characteristic form, possessing a well-behaved fundamental solution . These characterizations are based on suitable average operators on the level sets of . Asymptotic characterizations are also considered, extending classical results of Blaschke, Privaloff, Radó, Beckenbach, Reade and Saks. We analyze as well the notion of subharmonic function...
Subharmonic Functions on Real and Complex Manifolds.
Sur les fonctions propres positives des variétés de Cartan-Hadamard.
Symmetry and Overdetermined Boundary Value Problems.
The boundary value problem for Dirac-harmonic maps
Dirac-harmonic maps are a mathematical version (with commuting variables only) of the solutions of the field equations of the non-linear supersymmetric sigma model of quantum field theory. We explain this structure, including the appropriate boundary conditions, in a geometric framework. The main results of our paper are concerned with the analytic regularity theory of such Dirac-harmonic maps. We study Dirac-harmonic maps from a Riemannian surface to an arbitrary compact Riemannian manifold. We...
The Poisson boundary for rank one manifolds and their compact lattices.
The Poisson integral for a ball in spaces of constant curvature
We present explicit expressions of the Poisson kernels for geodesic balls in the higher dimensional spheres and real hyperbolic spaces. As a consequence, the Dirichlet problem for the projective space is explicitly solved. Comparison of different expressions for the same Poisson kernel lead to interesting identities concerning special functions.
The Poisson summation formula for a Dirichlet problem with gliding and glancing rays
Theory of Bessel potentials. III : potentials on regular manifolds
In this paper Bessel potentials on -Riemannian manifolds (open or bordered) are studied. Let be an -dimensional manifold, and a submanifold of of dimension . Sufficient conditions are given for: 1) the restriction to of any potential of order on to be a potential of order on ; 2) any potential of order on to be extendable to a potential of order on . It is also proved that for a bordered manifold the restriction to its interior is an isometric isomorphism between the...
Uniqueness and Stability of Harmonic Maps and Their Jacobi Fields.
Uniqueness of nonnegative solutions of the Cauchy problem for parabolic equations on manifolds or domains
Некоторые свойства трубчатых минимальных поверхностей произвольной коразмерности
О лиувиллевых теоремах для гармонических функций с конечным интегралом Дирихле
О существовании положительных фундаментальных решений уравнения Лапласа на римановых многообразиях
Теория потенциала на однородных группах