On the Legendre and Laplace transformations
On the Liouville property for sublaplacians
On the logarithmic potential defined for a Van Koch curve.
On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold
The Martin compactification of a bounded Lipschitz domain is shown to be for a large class of uniformly elliptic second order partial differential operators on .Let be an open Riemannian manifold and let be open relatively compact, connected, with Lipschitz boundary. Then is the Martin compactification of associated with the restriction to of the Laplace-Beltrami operator on . Consequently an open Riemannian manifold has at most one compactification which is a compact Riemannian...
On the mean value property of finely harmonic and finely hyperharmonic functions.
On the multivariate transfinite diameter
We prove several new results on the multivariate transfinite diameter and its connection with pluripotential theory: a formula for the transfinite diameter of a general product set, a comparison theorem and a new expression involving Robin's functions. We also study the transfinite diameter of the pre-image under certain proper polynomial mappings.
On the Neumann Problem for the Nonlinear Parabolic Equation of Eells-Sampson and Harmonie Mappings.
On the optimal growth of functions with bounded Laplacian.
On the orthogonal projections onto spaces of pluriharmonic functions and duality
On the Poisson equation in the potential theory of a single kernel.
On the Poisson integral for Lipschitz and -domains
On the rank of harmonic maps.
On the relation between elliptic and parabolic Harnack inequalities
We show that, if a certain Sobolev inequality holds, then a scale-invariant elliptic Harnack inequality suffices to imply its a priori stronger parabolic counterpart. Neither the relative Sobolev inequality nor the elliptic Harnack inequality alone suffices to imply the parabolic Harnack inequality in question; both are necessary conditions. As an application, we show the equivalence between parabolic Harnack inequality for on , (i.e., for ) and elliptic Harnack inequality for on .
On the representation of Dirichlet forms
A general representation theorem is obtained for positive quadratic forms, defined on (the space of continuously differentiable functions with compact support contained in ) which are local and on which all normal contractions operate.
On the sense preserving mappings in the Helm topology in the plane
∗Research supported by the grant No. GAUK 186/96 of Charles University.We introduce the helm topology in the plane. We show that (assuming the helm local injectivity and the Euclidean continuity) each mapping which is oriented at all points of a helm domain U is oriented at U.
On the Skew Product of Symmetric Diffusion Processes.
On the structure of subordinate semigroups.
On the volume of a pseudo-effective class and semi-positive properties of the Harder-Narasimhan filtration on a compact Hermitian manifold
This paper divides into two parts. Let (X,ω) be a compact Hermitian manifold. Firstly, if the Hermitian metric ω satisfies the assumption that for all k, we generalize the volume of the cohomology class in the Kähler setting to the Hermitian setting, and prove that the volume is always finite and the Grauert-Riemenschneider type criterion holds true, which is a partial answer to a conjecture posed by Boucksom. Secondly, we observe that if the anticanonical bundle is nef, then for any ε >...
On unicity of the Riesz decomposition of an excessive measure.
One-dimensional random walks, decreasing rearrangements and discrete Steiner symmetrization