Related papers: Global perturbation potential function on complete…

We study properties of irreducible and completely reducible representations of finitely generated groups Gamma into reductive algebraic groups G in in the context of the geometric invariant theory of the G-action on Hom(Gamma,G) by…

We prove a Liouville theorem for the plurisubharmonic functions on complete Kaelher manifolds. As the applications, we prove a splitting theorem for complete Kaehler manifolds with nonnegative biscetional curvature in terms of the linear…

We consider the Laplace-Beltrami operator $\Delta_g$ on a smooth, compact Riemannian manifold $(M,g)$ and the determinantal point process $\mathcal{X}_{\lambda}$ on $M$ associated with the spectral projection of $-\Delta_g$ onto the…

If a mapping of several complex variables into projective space is holomorphic in each pair of variables, then it is globally holomorphic.

Let $M$ be a $n$-dimensional complex manifold and $f,g:M\to M$ two distinct holomorphic self-maps. Suppose that $f$ and $g$ coincide on a globally irreducible compact hypersurface $S\subset M$. We show that if one of the two maps is a local…

Closed-form expressions for the singular-potential integrals <m| x^-alpha |n> are obtained with respect to the Gol'dman and Krivchenkov eigenfunctions for the singular potential V(x) = B x^2 + A/x^2, B > 0, A >= 0. These formulas are…

A relatively polynomially convex subset $V$ of a domain $\Omega$ has the extension property if for every polynomial $p$ there is a bounded holomorphic function $\phi$ on $\Omega$ that agrees with $p$ on $V$ and whose $H^\infty$ norm on…

Let $G$ be a locally compact abelian topological group. For locally bounded measurable functions $\varphi: G\to\Bbb {C}$ we discuss notions of spectra for $\varphi$ relative to subalgebras of $L^{1}(G)$. In particular we study polynomials…

A new type of exact solvability is reported. We study the general central polynomial potentials (with 2q anharmonic terms) which satisfy the Magyari's partial exact solvability conditions (this means that they possess a…

In the framework of started in Ref.[1] construction procedure of the general superfield quantization method for gauge theories in Lagrangian formalism the rules for Hamiltonian formulation of general superfield theory of fields (GSTF) are…

We study the existence of global implicit functions for equations defined on open subsets of Banach spaces. The partial derivative with respect to the second variable is only required to have a left inverse instead of being invertible.…

We consider the functional \[ F(u)=\int_{\Omega} f(\nabla u)\,dx\qquad u\in\varphi+W^{1,1}_0(\Omega) \] where $\Omega$ is a Lipschitz bounded open set of $\R^N$, $f:\R^N\to\R\cup \{+\infty\}$ is a superlinear Borel function, $\varphi\in…

In this paper, using the theory developed in [8], we obtain some results of a totally new type about a class of non-local problems. Here is a sample: Let $\Omega\subset {\bf R}^n$ be a smooth bounded domain, with $n\geq 4$, let $a, b,…

We show that the holonomy invariance of a function on the tangent bundle of a manifold, together with very mild regularity conditions on the function, is equivalent to the existence of local parallelisms compatible with the function in a…

We study global deformations of certain projective bundles over projective spaces. We show that any projective global deformation of a projective bundle over $\bP^1$ carries the structure of a projective bundle over some projective space.…

This note is an addendum to the paper `Global pluripotential theory over a trivially valued field' by the present authors, in which we prove two results. Let $X$ be an irreducible projective variety over an algebraically closed field field…

We formulate the full bosonic SL(5) exceptional field theory in a coordinate-invariant manner. Thereby we interpret the 10-dimensional extended space as a manifold with $\mathrm{SL}(5)\times\mathbb{R}^+$-structure. We show that the algebra…

Let $X$ be a compact K\"ahler manifold and $\theta$ a smooth closed $(1,1)$-real form representing a big cohomology class $\alpha \in H^{1,1}(X,\R)$. The purpose of this note is to show, using pluripotential and viscosity techniques, that…

This note is concerned with some essential properties (optimal isoperimetry, first variation, and monotonicity formula) of the so-called $[0,1)\ni\gamma$-torsional rigidity $\mathcal{T}_{\gamma,\mathsf{g}}$ on a complete Riemannian…

We prove the existence of holomorphic functions $f$ defined on any open convex subset ${\rm \Omega}\subset {{\mathbb C}}^n$, whose partial sums of the Taylor developments approximate uniformly any complex polynomial on any convex compact…