Related papers: Vertical perimeter versus horizontal perimeter

For a singular Riemannian foliation $\mathcal{F}$ on a Riemannian manifold, a curve is called horizontal if it meets the leaves of $\mathcal{F}$ perpendicularly. For a singular Riemannian foliation $\mathcal{F}$ on a unit sphere…

In this paper we prove that isoperimetric sets in three-dimensional homogeneous spaces diffeomorphic to $\mathbb{R}^3$ are topological balls. We also prove that in three-dimensional homogeneous spheres isopermetric sets are either…

Compact quantum metric spaces are order unit spaces along with a Lip norm. On the order unit space of the selfadjoint elements of the dense subalgebra of smooth elements in the quantum Heisenberg manifold we construct Lip norms.

We prove $L^p$-Hardy inequalities with distance to the boundary for domains in the Heisenberg group ${\mathbb{H}}^n$, $n\geq 1$. Our results are based on a certain geometric condition. This is first implemented for the Euclidean distance in…

We study functions of bounded variation (and sets of finite perimeter) on a convex open set $\Omega\subseteq X$, $X$ being an infinite dimensional real Hilbert space. We relate the total variation of such functions, defined through an…

Let $\Omega$ be an open convex set in ${\mathbb R}^m$ with finite width, and let $v_{\Omega}$ be the torsion function for $\Omega$, i.e. the solution of $-\Delta v=1, v\in H_0^1(\Omega)$. An upper bound is obtained for the product of $\Vert…

The Heisenberg curve is defined topologically as a cover of the Fermat curve and corresponds to an extension of the projective line minus three points by the non-abelian Heisenberg group modulo n. We compute its fundamental group and…

Perivolaropoulos has recently proposed a position-deformed Heisenberg algebra which includes a maximal length [Phys.Rev.95, 103523 (2017)]. He has shown that this length scale naturally emerges in the context of cosmological particle's…

In this article we consider a certain distinguished set $U(\Omega,m) \subseteq \{1,2,\ldots,2g+1,\infty\}$ that can be attached to a marked hyperelliptic curve of genus $g$ equipped with a small period matrix $\Omega$ for its polarized…

We extend the notion of an $H$-normal quotient digraph of an $H$-vertex-transitive digraph to that of an $H$-subnormal quotient digraph. Using these concepts, together with bipartite halves of bipartite digraphs, we show that, for each…

Let $\h_n$ be the $(2n+1)$-dimensional Heisenberg group. and let ${\cal L}_\alpha$ be the sublaplacian of the Lie algebra of $\h_n$ A new spherical harmonics with its orthogonal polynomial properties is presented for the group.

Let $V$ be a $2n$-dimensional vector space over a field $F$ and $\Omega$ be a non-degenerate symplectic form on $V$. Denote by ${\mathfrak H}_{k}(\Omega)$ the set of all $2k$-dimensional subspaces $U\subset V$ such that the restriction…

The space of directions is a notion of boundary associated to an arbitrary totally disconnected locally compact group. We explicitly calculate the space of directions of a group acting vertex transitively with compact open vertex…

We prove some new a priori estimates for H_2-convex functions which are zero on the boundary of a bounded smooth domain \Omega in a Carnot group G. Such estimates are global and are geometric in nature as they involve the horizontal mean…

We prove that in the Heisenberg group $\mathbb{H}^1$ with a sub-Finsler structure, an $(X,Y)$-Lipschitz surface which is complete, oriented, connected and stable must be a vertical plane. In particular, the result holds for entire intrinsic…

We characterize helix surfaces in the Berger sphere, that is surfaces which form a constant angle with the Hopf vector field. In particular, we show that, locally, a helix surface is determined by a suitable 1-parameter family of isometries…

A unitary representation of a, possibly infinite dimensional, Lie group G is called semi-bounded if the corresponding operators id\pi(x) from the derived representations are uniformly bounded from above on some non-empty open subset of the…

Let $ 1 \rightarrow N \rightarrow G \rightarrow Q \rightarrow 1$ be an exact sequence of finitely presented groups where Q is infinite and not virtually cyclic, and is the fundamental group of some closed 3-manifold. If G is Kaehler, we…

In the uniformly discrete case of virtual persistence diagram groups $K(X,A)$, we construct a translation-invariant heat semigroup. The kernels are supported on a countable subgroup $H$, and the restriction to $H$ has Fourier exponent…

We study the geometry and dynamics of discrete subgroups $\Gamma$ of $\PSL(3,\mathbb{C})$ with an open invariant set $\Omega \subset \PC^2$ where the action is properly discontinuous and the quotient $\Omega/\Gamma$ contains a connected…