Related papers: Lemma Poincar\'e for L_infty,loc - forms
We give a new self-contained proof of Poincar\'e's Polyhedron Theorem on presentations of discontinuous groups of isometries of a Riemann manifold of constant curvature. The proof is not based on the theory of covering spaces, but only…
We classify the possible behaviour of Poincar\'e-Dulac normal forms for dynamical systems in $R^n$ with nonvanishing linear part and which are equivariant under (the fundamental representation of) all the simple compact Lie algebras and…
Based on the framework of Koch-Lamm and tensor heat kernel estimates, we obtain a uniform proof of the short-time existence, uniqueness, and continuous dependence for Ricci flows starting from a complete Riemannian metric with bounded…
Using hyperbolic form convolution with doubly isometry-invariant kernels, the explicit expression of the inverse of the de Rham laplacian acting on m-forms in the Poincar\'{e} space is found. Also, by means of some estimates for hyperbolic…
We prove that every perfect torsion theory for a ring $R$ is differential (in the sense of [P. E. Bland, Differential torsion theory, Journal of Pure and Applied Algebra 204 (2006) 1 -- 8]). In this case, we construct the extension of a…
Pure spinor formalism and non-integrable exponential factors are used for constructing the conformal-invariant wave equation and Lagrangian density for massive fermion. It is proved that canonical Dirac Lagrangian for massive fermion is…
Starting from the problem of describing cohomological invariants of Poisson manifolds we prove in a sense a ``no-go'' result: the differential graded Lie algebra of de Rham forms on a smooth Poisson manifold is formal.
The Dirac approach to constrained systems can be adapted to construct relativistic invariant theories on a noncommutative (NC) space. As an example, we propose and discuss relativistic invariant NC particle coupled to electromagnetic field…
We give a sharp condition on the lower local Lipschitz constant of a mapping from a metric space supporting a Poincar\'e inequality to a Banach space with the Radon-Nikodym property that guarantees differentiability at almost every point.…
We introduce smooth L^\infty differential forms on a singular (semialgebraic) set X in R^n. Roughly speaking, a smooth L^\infty differential form is a certain class of equivalence of 'stratified forms', that is, a collection of smooth forms…
We lift upper and lower estimates from linear functionals to $n$-homogeneous polynomials and using this result show that $l_\infty$ is finitely represented in the space of $n$-homogeneous polynomials, $n\ge2$, for any infinite dimensional…
We discuss some of the key ideas of Perelman's proof of Poincar\'e's conjecture via the Hamilton program of using the Ricci flow, from the perspective of the modern theory of nonlinear partial differential equations.
Lurie's theorem states that there exists a sheaf of ring spectra on the site of formally \'etale Deligne--Mumford stacks over the moduli stack of $p$-divisible groups of height $n$, which agrees with the classical Landweber exact functor…
We prove that there is no nontrivial $L^2$-integrable harmonic 1-form on noncompact complete gradient steady Ricci solitons or noncompact complete gradient shrinking K\"{a}hler-Ricci solitons. As an application, it can be used to…
An analogue of Rellich's theorem is proved for discrete Laplacian on square lattice, and applied to show unique continuation property on certain domains as well as non-existence of embedded eigenvalues for discrete Schr{\"o}dinger…
The classical Poincar\'e inequality establishes that for any bounded regular domain $\Omega\subset \R^N$ there exists a constant $C=C(\Omega)>0$ such that $$ \int_{\Omega} |u|^2\, dx \leq C \int_{\Omega} |\nabla u|^2\, dx \ \ \forall u \in…
A PDE proof is provided for the sharp $L^\infty$ estimates for the complex Monge-Amp\`ere equation which had required pluripotential theory before. The proof covers both cases of fixed background as well as degenerating background metrics.…
Symmetries in the Lagrangian formalism of arbitrary order are analysed with the help of the so-called Anderson-Duchamp-Krupka equations. For the case of second order equations and a scalar field we establish a polynomial structure in the…
We study the structure and dynamics of the infinite sequence of extensions of the Poincar{\'e} algebra whose method of construction was described in a previous paper [1]. We give explicitly the Maurer-Cartan (MC) 1-forms of the extended Lie…
The incompressible Navier-Stokes equations contain viscous dissipation but no thermal noise. I show, using a topological argument based on Poincar\'e's lemma, that the fluctuation-dissipation relation for the full nonlinear dynamics can be…