Related papers: $L^2$-extension of $\dbar$-closed forms

We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.

We prove that any closed map between metrizable spaces can be extended to a closed map between completely metrizable spaces with the same extensional dimension.

We generalize Iwasawa's theorem on class group over $\Z_p$-extensions to all $\Z_p^d$-extensions.

We study the existence of formal Taylor expansions for functions defined on fields of generalised series. We prove a general result for the existence and convergence of those expansions for fields equipped with a derivation and an…

An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.

In this paper, we develop $L^2$ theory for Riemannian and Hermitian foliations on manifolds with basic boundary. We establish a decomposition theorem, various vanishing theorems, a twisted duality theorem for basic cohomologies and an…

In the paper we investigate Borel classes of multivalued functions of two variables. In particular we generalize a result of Marczewski and Ryll-Nardzewski concerning of real function whose ones of its sections are right-continuous and…

We show that infinitesimal Torelli for $n$-forms holds for abelian covers of algebraic varieties of dimension $n\ge 2$, under some explicit ampleness assumptions on the building data of the cover. Moreover, we prove a variational Torelli…

The use of iteration and piecewise functions allows analytic expression of the trajectories of an R\"ossler-like attractor, avoiding infinite series solution. It seems possible to extend this approach to other attractors, even if the…

We obtain $\Omega$-results for linear exponential sums with rational additive twists of small prime denominators weighted by Hecke eigenvalues of Maass cusp forms for the group $\mathrm{SL}_3(\mathbb Z)$. In particular, our $\Omega$-results…

We prove Mazur and Rubin's Iwasawa-theoretic Gross-Zagier conjecture (under some restrictive hypotheses), which relates Heegner points in towers of number fields to the 2-variable p-adic L-function. The result generalizes Perrin-Riou's…

We revisit certain localised variants of the Bennett-Carbery-Tao multilinear restriction theorem, recently proved by Bejenaru. We give a new proof of Bejenaru's theorem, relating the estimates to the theory of Kakeya-Brascamp-Lieb…

We prove a finiteness result for dominant rational maps whose orbifold base is of general type. Our finiteness result generalizes Maehara's theorem that a given variety dominates only finitely many projective varieties of general type up to…

We prove an analog of the classical Hartogs extension theorem for CR $L^{2}$ functions defined on boundaries of certain (possibly unbounded) domains on coverings of strongly pseudoconvex manifolds. Our result is related to a problem posed…

We establish a quantitative version of Oppenheim's conjecture for generic ternary indefinite quadratic forms using an analytic number theory approach. The statements come with power gains and in some cases are essentially optimal

We prove a uniform version of the Goldblatt-Thomason theorem for logics algebraically captured by normal lattice expansions (normal LE-logics).

Let p be a prime number. We compute the Yoneda extension algebra of $GL_2$ over an algebraically closed field of characteristic p by developing a theory of Koszul duality for a certain class of 2-functors, one of which controls the category…

We give a short and self-contained proof of the Marker-Steinhorn Theorem for o-minimal expansions of ordered groups, based on an analysis of linear orders definable in such structures.

Yet another proof of Onsager-Machlup formula for diffusion processes on a Riemannian manifold after Takahashi-Watanabe, Fujita-Kotani. The proof is purely probabilistic and contains a precise study on an ergodic effect for a key Wiener…

Let $(\mathcal{M},g_0)$ be a compact Riemannian manifold-with-boundary. We present a new proof of the classical Gaffney's inequality for differential forms in boundary value spaces over $\mathcal{M}$, via the variational approach \`{a} la…