Related papers: Elliptic Boundary Value Problems and Partial Group…

Suppose $\Gamma^{+}$ is the positive cone of a totally ordered abelian group $\Gamma$, and $(A,\Gamma^{+},\alpha)$ is a system consisting of a $C^*$-algebra $A$, an action $\alpha$ of $\Gamma^{+}$ by extendible endomorphisms of $A$. We…

We consider the Dirichlet-to-Neumann operator associated to a strictly elliptic operator on the space $\mathrm{C}(\partial M)$ of continuous functions on the boundary $\partial M$ of a compact manifold $\overline{M}$ with boundary. We prove…

We consider smooth actions of lattices in higher-rank semisimple Lie groups on manifolds. We define two numbers $r(G)$ and $m(G)$ associated with the roots system of the Lie algebra of a Lie group $G$. If the dimension of the manifold is…

We prove that the crossed product $C^*$-algebra $C^*_r(\Gamma,\partial\Gamma)$ of a free group $\Gamma$ with its boundary $\partial\Gamma$ naturally sits between the reduced group $C^*$-algebra $C^*_r\Gamma$ and its injective envelope…

Let $\Gamma$ be a finitely generated group which admits an action by homeomorphisms on a compact metrizable space $X$. We show that there is a metric on $X$ defining the original topology such that for this metric, the action is by…

We consider special elliptic operators in functional spaces on manifolds with a boundary which has some singular points. Such an operator can be represented by a sum of operators, and for a Fredholm property of an initial operator one needs…

We consider a nonlinear version of the Yamabe problem on locally conformally flat compact manifolds with boundary. The main technique we used is to derive boundary $C^2$ estimates directly from boundary $C^0$ estimates. In particular, the…

We show that if $\Gamma\curvearrowright (X^\Gamma,\mu^\Gamma)$ is a Bernoulli action of an i.c.c. nonamenable group $\Gamma$ which is weakly amenable with Cowling-Haagerup constant $1$, and $\Lambda\curvearrowright(Y,\nu)$ is a free ergodic…

We study topological quivers $Q$ admitting a free and proper action by a locally compact group $G$ together with their associated $C^*$-algebras. On the topological side, we provide a complete classification of topological quivers which…

Let $M$ be a compact Riemannian manifold with boundary $\pp M$ and $L= \DD+Z$ for a $C^1$-vector field $Z$ on $M$. Several equivalent statements, including the gradient and Poincar\'e/log-Sobolev type inequalities of the Neumann semigroup…

We prove that for any countable acylidrically hyperbolic group $G$, there exists a generating set $S$ of $G$ such that the corresponding Cayley graph $\Gamma(G,S)$ is hyperbolic, $|\partial\Gamma(G,X)|>2$, the natural action of $G$ on…

Let $G$ be a simply connected, connected completely solvable Lie group with Lie algebra $\mathfrak{g}=\mathfrak{p}+\mathfrak{m}.$ Next, let $\pi$ be an infinite-dimensional unitary irreducible representation of $G$ obtained by inducing a…

We investigate elliptic boundary-value problems with additional unknown functions in boundary conditions. These problems were introduced by Lawruk. We prove that the operator corresponding to such a problem is bounded and Fredholm on…

In previous work arXiv:2407.13556, we proposed an extended phase space structure at null infinity accommodating large gauge symmetries for sub$^n$-leading soft theorems in Yang-Mills, via dressing fields arising in the Stueckelberg…

In this paper, we study the existence of nontrivial solutions of the Dirichlet boundary value problem for the following elliptic system: \begin{equation} \left\{ \begin{aligned} -\Delta u & = au + bv + f(x,u,v); &\quad\mbox{ for…

Let $\Gamma$ be a discrete icc subgroup of PSL(2,R) of infinite covolume. and let M denote the quotient of the unit disc by $\Gamma$. We prove that a Toeplitz operator with $\Gamma$-invariant symbol f in C(M) is Brauer Fredholm if its…

In this paper operator pencils $A(x,D,\lambda)$ are investigated which depend polynomially on the parameter $\lambda$ and act on a manifold with boundary. The operator A is assumed to satisfy the condition of N-ellipticity with parameter…

In this paper, we study boundary actions of CAT(0) spaces from a point of view of topological dynamics and $C^*$-algebras. First, we investigate the actions of right-angled Coexter groups and right-angled Artin groups with finite defining…

We deal with existence and uniqueness of positive solutions of an elliptic boundary value problem modeled by \begin{equation*} \begin{cases} \displaystyle -\Delta_p u= \frac{f}{u^\gamma} + g u^q & \mbox{in $\Omega$,} \\ u = 0 & \mbox{on…

Let M be a Riemann surface with boundary $\partial M$ and genus greater than zero. Let $\Gamma$ be the mapping class group of M fixing $\partial M$. The group $\Gamma$ acts on ${\mathcal M}_{\mathcal C} = \Hom_{\mathcal…