相关论文: A subelliptic Taylor isomorphism on infinite-dimen…

In this paper we shall study smooth submanifolds immersed in a k-step Carnot group G of homogeneous dimension Q. Among other results, we shall prove an isoperimetric inequality for the case of a $C^2$-smooth compact hypersurface S with - or…

The full solenoid over a topological space $X$ is the inverse limit of all finite covers. When $X$ is a compact Hausdorff space admitting a locally path connected universal cover, we relate the pointed homotopy equivalences of the full…

In this paper we study heat kernels associated to a Carnot group $G$, endowed with a family of collapsing left-invariant Riemannian metrics $\sigma_\e$ which converge in the Gromov-Hausdorff sense to a sub-Riemannian structure on $G$ as…

We first show that hypergeometric functions appear naturally as spectral functions when applying pseudo-differential calculus to decipher heat kernel asymptotic in the situation where the symbol algebra is noncommutative. Such observation…

An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…

We classify the effective and transitive actions of a Lie group $G$ on an n-dimensional non-degenerate hyperboloid (also called real pseudo-hyperbolic space), under the assumption that $G$ is a closed, connected Lie subgroup of…

We prove asymptotically isometric, coarsely geodesic metrics on a toral relatively hyperbolic group are coarsely equal. The theorem applies to all lattices in SO(n,1). This partly verifies a conjecture by Margulis. In the case of hyperbolic…

We start from a noncompact Lie algebra isomorphic to the Dirac algebra and relate this Lie algebra in a brief review to low energy hadron physics described by the compact group SU(4). This step permits an overall physical identification of…

We provide the full theory of thermodynamic formalism for a very general collection of entire functions in class $\mathcal B$. This class overlaps with the collection of all entire functions for which thermodynamic formalism has been so far…

Symmetries in quantum mechanics are realized by the projective representations of the Lie group as physical states are defined only up to a phase. A cornerstone theorem shows that these representations are equivalent to the unitary…

We detect Hilbert manifolds among isometrically homogeneous metric spaces and apply the obtained results to recognizing Hilbert manifolds among homogeneous spaces of the form G/H where G is a metrizable topological group and H is a closed…

We establish dimension-independent estimates related to heat operators e^{tL} on manifolds. We first develop a very general contractivity result for Markov kernels which can be applied to diffusion semigroups. Second, we develop estimates…

We study holomorphic isometries between bounded symmetric domains with respect to the Bergman metrics up to a normalizing constant. In particular, we first consider a holomorphic isometry from the complex unit ball into an irreducible…

For any n-dimensional compact Riemannian manifold (M,g), we construct a canonical t-family of isometric embeddings I_{t}: M->R^{q(t)}, with t>0 sufficiently small and q(t)>>t^{-n/2}. This is done by intrinsically perturbing the heat kernel…

A well-known Hurewicz-type formula for asymptotic-dimension-lowering group homomorphisms, due to A. Dranishnikov and J. Smith, states that if $f:G\to H$ is a group homomorphism, then $\mathrm{asdim} G \leq \mathrm{asdim} H + \mathrm{asdim}…

Products of Siegel upper half spaces are Siegel domains, whose Silov boundaries have the structure of products $\mathscr H_1\times\mathscr H_2$ of Heisenberg groups. By the reproducing formula of bi-parameter heat kernel associated to…

By decomposing the regular representation of a particular (Heisenberg-like) Lie supergroup into irreducible subspaces, we show that not all of them can be obtained by applying geometric quantization to coadjoint orbits with an even…

A group $G$ is integrable if it is isomorphic to the derived subgroup of a group $H$; that is, if $H'\simeq G$, and in this case $H$ is an integral of $G$. If $G$ is a subgroup of $U$, we say that $G$ is integrable within $U$ if $G=H'$ for…

Representations of CCR algebras in spaces of entire functions are classified on the basis of isomorphisms between the Heisenberg CCR algebra A_H and star algebras of holomorphic operators. To each representations of such algebras,…

The present work stemmed from the study of the problem of harmonic analysis on the infinite-dimensional unitary group U(\infty). That problem consisted in the decomposition of a certain 4-parameter family of unitary representations, which…