相关论文: On the moduli space of quasi-homogeneous functions

Let $\frak g$ be a reductive Lie algebra over an algebraically closed field of characteristic $p>0$. In this paper, we study the representations of $\frak g$ with a $p$-character $\chi$ of standard Levi form associated with a given subset…

Let G be a Lie group and g its Lie algebra. We develop a theory of quasi Poisson structures relative to a not necessarily non-degenerate Ad-invariant symmetric 2-tensor in the tensor square of g and one of general not necessarily…

Given a $\mathfrak{g}$-action on a Poisson manifold $(M, \pi)$ and an equivariant map $J: M \rightarrow \mathfrak{h}^*,$ for $\mathfrak{h}$ a $\mathfrak{g}$-module, we obtain, under natural compatibility and regularity conditions previously…

We introduce the volume-preserving equivalence among symmetric matrix-valued map-germs which is the unimodular version of Bruce's $\mathcal{G}$-equivalence. The key concept to deduce unimodular classification out of classification relative…

We construct an invariant of the bi-Lipschitz contact equivalence of continuous function germs definable in a polynomially bounded o-minimal structure, such as semialgebraic functions. For a germ $f,$ the invariant is given in terms of the…

We give a rigorous account and prove continuity properties for the correspondence between almost flat bundles on a triangularizable compact connected space and the quasi-representations of its fundamental group. For a discrete countable…

In this paper we study the Plancherel formula for a new class of homogeneous spaces for real reductive Lie groups; these spaces are fibered over non-Riemannian symmetric spaces, and they exhibit a phenomenon of uniform infinite…

The investigation of symmetries of b-symplectic manifolds and folded-symplectic manifolds is well-understood when the group under consideration is a torus (see, for instance, [GMPS,GLPR, GMW18a] for b-symplectic manifolds and [CGP, CM] for…

We prove the density of smooth functions in the modular topology in the Musielak-Orlicz-Sobolev spaces essentially extending the results of Gossez \cite{GJP2} obtained in the Orlicz-Sobolev setting. We impose new systematic regularity…

We characterize cofinally Bourbaki quasi-complete metric spaces and their completions in terms of certain Lipschitz-type functions. To this end, we introduce and study a new class of functions, namely strongly uniformly locally Lipschitz…

We study the structure of families of well approximable elements of tensor products of Banach spaces including analogs of the classical quasianalytic classes in the sense of Bernstein and Beurling. As in the case of quasianalytic functions,…

For any open, connected and bounded set $\Omega \subseteq \mathbb C^m$, let $\mathcal A$ be a natural function algebra consisting of functions holomorphic on $\Omega$. Let $\mathcal M$ be a Hilbert module over the algebra $\mathcal A$ and…

In this paper we introduce the concept of Wiener-Luxemburg amalgam spaces which are a modification of the more classical Wiener amalgam spaces intended to address some of the shortcomings the latter face in the context of…

We prove that nonnegative almost minimizers of the horizontal Bernoulli-type functional $$ J(u,\Omega):=\int_{\Omega}\Big(|\nabla_{\mathbb{G}} u(x)|^2+\chi_{\{u>0\}}(x)\Big)\,dx$$ are Lipschitz continuous in the intrinsic sense.

We consider quasi-polynomial spaces of differential forms defined as weighted (with a positive weight) spaces of differential forms with polynomial coefficients. We show that the unisolvent set of functionals for such spaces on a simplex in…

Tukia and Vaisala showed that every quasi-conformal map of $\R^n$ extends to a quasi-conformal self-map of $\R^{n+1}$. The restriction of the extended map to the upper half-space $\R^n \times \R^+$ is, in fact, bi-Lipschitz with respect to…

We construct a compactification of the moduli space of twisted holomorphic maps with varying complex structure and bounded energy. For a given compact symplectic manifold $X$ with a compatible complex structure and a Hamiltonian action of…

A classical theorem of Titchmarsh relates the $L^2$-Lipschitz functions and decay of the Fourier transform of the functions. In this note, we prove the Titchmarsh theorem for Damek-Ricci space (also known as harmonic $NA$ groups) via moduli…

Let $(X, \omega)$ be a compact symplectic manifold and $L$ be a Lagrangian submanifold. Suppose $(X, L)$ has a Hamiltonian $S^1$ action with moment map $\mu$. Take an invariant $\omega$-compatible almost complex structure, we consider…

This article introduces a universal moduli space for the set whose archetypal element is a pair that consists of a metric and second fundamental form from a compact, oriented, positive genus minimal surface in some hyperbolic 3-manifold.…