Related papers: Complex Hessian measures with respect to a backgro…
This paper extends the nonabelian Hodge correspondence for Kaehler manifolds to a larger class of hermitian metrics on complex manifolds called balanced of Hodge-Riemann type. Essentially, it grows out of a few key observations so that the…
The existence of quasi-bi-Hamiltonian structures for the Kepler problem is studied. We first relate the superintegrability of the system with the existence of two complex functions endowed with very interesting Poisson bracket properties…
Mainly motivated by a conjecture of Alesker and Verbitsky, we study a class of fully non-linear elliptic equations on certain compact hyperhermitian manifolds. By adapting the approach of Sz\'{e}kelyhidi to the hypercomplex setting, we…
Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is…
We propose to study deformation quantizations of Whitney functions. To this end, we extend the notion of a deformation quantization to algebras of Whitney functions over a singular set, and show the existence of a deformation quantization…
This work extends the Mond-Pecaric method to functions with multiple operators as arguments by providing arbitrarily close approximations of the original functions. Instead of using linear functions to establish lower and upper bounds for…
This article summarises the theory of several bounded functional calculi for unbounded operators that have recently been discovered. The extend the Hille--Phillips calculus for (negative) generators $A$ of certain bounded $C_0$-semigroups,…
In this paper, we concern with the existence of solutions of the weighted complex $m$-Hessian equation $-\chi(u)H_{m}(u)=\mu$ in the class $\mathcal{E}_{m,\chi}(f,\Omega)$ if there exists subsolution in this class, where the given boundary…
In this paper, we study a special exhaustion function on almost Hermitian manifolds and establish the existence result by using the Hessian comparison theorem. From the viewpoint of the exhaustion function, we establish related Schwarz type…
K-Theory for hermitian symmetric spaces of non-compact type, as developed recently by the authors, allows to put Cartan's classification into a homological perspective. We apply this method to the case of inductive limits of finite…
We introduce a class of hermitian metrics with {\em Lee potential}, that generalize the notion of l.c.K. metrics with potential introduced in \cite{ov} and show that in the classical examples of Calabi and Eckmann of complex structures on…
Given a charge and current distribution with compact support, the associated potentials and fields are generally not integrable in the classical sense. However, it is convenient to be able to define their Fourier transform in order to…
Potential functional approximations are an intriguing alternative to density functional approximations. The potential functional that is dual to the Lieb density functional is defined and properties given. The relationship between…
In this paper we consider a complete connected noncompact Riemannian manifold M with Ricci curvature bounded from below and positive injectivity radius. Denote by L the Laplace-Beltrami operator on M. We assume that the kernel associated to…
I give a brief overview of the mathematical theory of Noether symmetries of multifield cosmological models, which decompose naturally into visible and Hessian (a.k.a. 'hidden') symmetries. While visible symmetries correspond to those…
Using pluricomplex Green functions we introduce a compactification of a complex manifold $M$ invariant with respect to biholomorphisms similar to the Martin compactification in the potential theory. For this we show the existence of a…
In this paper, we introduce the class $\mathcal{E}_{m,F}(\Omega)$ and solve complex $m$-Hessian equations in the class $\mathcal{E}_{m,F}(\Omega)$. Afterthat, we study subextension in the class $\mathcal{E}_{m,F}(\Omega)$ with the weighted…
In this paper, we introduce finite energy classes of quaternionic $m$-plurisubharmonic functions of Cegrell type and define the quaternionic $m$-Hessian operator on some Cegrell's classes. We use the variational approach to solve the…
We study semifinite harmonic functions on arbitrary branching graphs. We give a detailed exposition of an algebraic method which allows one to classify semifinite indecomposable harmonic functions on some multiplicative branching graphs.…
We show that the tools recently introduced by the first author in [9] allow to give a PDE description of p-harmonic functions in metric measure setting. Three applications are given: the first is about new results on the sheaf property of…