A family of exactly solvable radial quantum systems on space of non-constant curvature with accidental degeneracy in the spectrum.
A note on p-subharmonic functions on complete manifolds.
Biharmonic Green domains in a Riemannian manifold
Let be a Riemannian manifold without a biharmonic Green function defined on it and a domain in . A necessary and sufficient condition is given for the existence of a biharmonic Green function on .
Boundary value problems and layer potentials on manifolds with cylindrical ends
We study the method of layer potentials for manifolds with boundary and cylindrical ends. The fact that the boundary is non-compact prevents us from using the standard characterization of Fredholm or compact pseudo-differential operators between Sobolev spaces, as, for example, in the works of Fabes-Jodeit-Lewis and Kral-Wedland . We first study the layer potentials depending on a parameter on compact manifolds. This then yields the invertibility of the relevant boundary integral operators in the...
Characterisations of Poisson integrals on symmetric spaces.
Conformality and Pseudo-Riemannian Manifolds.
Convergence of martingales on manifolds of negative curvature
Cramér's formula for Heisenberg manifolds
Let be the error term in Weyl’s law for a 3-dimensional Riemannian Heisenberg manifold. We prove that , where is a specific nonzero constant and is an arbitrary small positive number. This is consistent with the conjecture of Petridis and Toth stating that .The idea of the proof is to use the Poisson summation formula to write the error term in a form which can be estimated by the method of the stationary phase. The similar result will be also proven in the -dimensional case.
Examples in the Classification Theory of Riemannian Manifolds and the Equation ...u = Pu.
Existence of positive harmonic functions on groups and on covering manifolds
Existence of quasi-isometric mappings and Royden compactifications.
Fatou and Littlewood related theorems and a convergence property in the R.S. Martin topology.
Fatou theorems and maximal functions for eigenfunctions of the Laplace-Beltrami operator in a bidisk.
Feynman-Kac formula, λ-Poisson kernels and λ-Green functions of half-spaces and balls in hyperbolic spaces
We apply the Feynman-Kac formula to compute the λ-Poisson kernels and λ-Green functions for half-spaces or balls in hyperbolic spaces. We present known results in a unified way and also provide new formulas for the λ-Poisson kernels and λ-Green functions of half-spaces in ℍⁿ and for balls in real and complex hyperbolic spaces.
Functional inequalities and manifolds with nonnegative weighted Ricci curvature
We show that -dimensional complete and noncompact metric measure spaces with nonnegative weighted Ricci curvature in which some Caffarelli-Kohn-Nirenberg type inequality holds are isometric to the model metric measure -space (i.e. the Euclidean metric -space). We also show that the Euclidean metric spaces are the only complete and noncompact metric measure spaces of nonnegative weighted Ricci curvature satisfying some prescribed Sobolev type inequality.
Generalized Dirac Operators on Nonsmooth Manifolds and Maxwell's Equations.
Harmonic morphisms and subharmonic functions.
Heat kernel on manifolds with ends
We prove two-sided estimates of heat kernels on non-parabolic Riemannian manifolds with ends, assuming that the heat kernel on each end separately satisfies the Li-Yau estimate.
Local Fatou theorem and the density of energy on manifolds of negative curvature.
Minimal Graphs.