On the space of Bloch harmonic functions and interpolation of spaces of harmonic and holomorphic functions
On the structure of subordinate semigroups.
On the structure of the conformal Gaussian curvature equation on R2. II.
On the support of the equilibrium measure for arcs of the unit circle and for real intervals.
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.
On univalent harmonic functions.
On univalent solutions of the biharmonic equation.
On V. I Smirnov domains.
On Veech's conjecture for harmonic functions
On weighed spaces
One-dimensional random walks, decreasing rearrangements and discrete Steiner symmetrization
Opérateurs carré du champ
Opérateurs dissipatifs et codissipatifs invariants par translations sur les groupes localement compacts
Operator-valued n-harmonic measure in the polydisc
An operator-valued multi-variable Poisson type integral is studied. In Section 2 we obtain a new equivalent condition for the existence of a so-called regular unitary dilation of an n-tuple T=(T₁,...,Tₙ) of commuting contractions. Our development in Section 2 also contains a new proof of the classical dilation result of S. Brehmer, B. Sz.-Nagy and I. Halperin. In Section 3 we turn to the boundary behavior of this operator-valued Poisson integral. The results obtained in this section improve upon...
Optimal conditions for anti-maximum principles
Optimal convex shapes for concave functionals
Motivated by a long-standing conjecture of Pólya and Szegö about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We then introduce a new algebraic structure on convex bodies, which allows to obtain global concavity and indecomposability results, and we discuss their application...
Optimal convex shapes for concave functionals
Motivated by a long-standing conjecture of Pólya and Szegö about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We then introduce a new algebraic structure on convex bodies, which allows to obtain global concavity and indecomposability results, and we discuss their application to isoperimetric-like inequalities. As a byproduct...
Optimal convex shapes for concave functionals
Motivated by a long-standing conjecture of Pólya and Szegö about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We then introduce a new algebraic structure on convex bodies, which allows to obtain global concavity and indecomposability results, and we discuss their application...
Optimal interface error estimates for the mean curvature flow