Related papers: Currents with corners and counting weighted triang…

We study conserved currents of any integer or half integer spin built from massless scalar and spinor fields in $AdS_3$. 2-forms dual to the conserved currents in $AdS_3$ are shown to be exact in the class of infinite expansions in higher…

We study the quantization of the corner symmetry algebra of 3d gravity, that is the algebra of observables associated with 1d spatial boundaries. In the continuum field theory, at the classical level, this symmetry algebra is given by the…

We investigate the mean curvature flows in a class of warped product manifolds with closed hypersurfaces fibering over $\mathbb{R}$. In particular, we prove that under natural conditions on the warping function and Ricci curvature bound for…

We prove that every locally Hamiltonian graph with $n\ge 3$ vertices and possibly with multiple edges has at least $3n-6$ edges with equality if and only if it triangulates the sphere. As a consequence, every edge-maximal embedding of a…

In this paper we study the ergodic theory and thermodynamic formalism of the geodesic flow on non-compact pinched negatively curved manifolds. We consider two notions of entropy at infinity, the topological and the measure theoretic entropy…

The purpose of this paper is to introduce a version of singular homology based on smooth mappings of manifolds with corners. Although variants of such a theory exists in the literature, we felt that certain points were not adequately…

In this paper we consider the anisotropic curve shortening flow in the plane in the presence of an ambient force. We consider force fields in which all their derivatives are bounded in the $L^{\infty}$ sense. We prove that closed embedded…

Extending the earlier results for analytic curve segments, in this article we describe the asymptotic behaviour of evolution of a finite segment of a C^n-smooth curve under the geodesic flow on the unit tangent bundle of a finite volume…

We show that symmetries and gauge symmetries of a large class of 2-dimensional sigma models are described by a new type of a current algebra. The currents are labeled by pairs of a vector field and a 1-form on the target space of the sigma…

In this paper we investigate the flow of surfaces by a class of symmetric functions of the principal curvatures with a mixed volume constraint. We consider compact surfaces without boundary that can be written as a graph over a sphere. The…

We discuss the sign of the persistent current of N electrons in one dimensional rings. Using a topology argument, we establish lower bounds for the free energy in the presence of arbitrary electron-electron interactions and external…

We investigate stationary torsional configurations supported by chiral Majorana neutrino currents in linearized gravity. A Ricci-flow-inspired geometric relaxation (with no physical time interpretation) is introduced to drive the metric…

This paper presents hyperbolic rank rigidity results for rank 1, nonpositively curved spaces. Let $M$ be a compact, rank 1 manifold with nonpositive sectional curvature and suppose that along every geodesic in $M$ there is a parallel vector…

We study $n$-dimensional area-minimizing currents $T$ in $\mathbb{R}^{n+1},$ with boundary $\partial T$ satisfying two properties: $\partial T$ is locally a finite sum of $(n-1)$-dimensional $C^{1,\alpha}$ orientable submanifolds which only…

We introduce the shifted inverse curvature flow in hyperbolic space. This is a family of hypersurfaces in hyperbolic space expanding by $F^{-p}$ with positive power $p$ for a smooth, symmetric, strictly increasing and $1$-homogeneous…

Exact metrics on some totally geodesic submanifolds of the moduli space of static hyperbolic N-vortices are derived. These submanifolds, denoted \Sigma_{n,m}, are spaces of C_n-invariant vortex configurations with n single vortices at the…

We consider integral area-minimizing $2$-dimensional currents $T$ in $U\subset \mathbb R^{2+n}$ with $\partial T = Q[\![\Gamma]\!]$, where $Q\in \mathbb N \setminus \{0\}$ and $\Gamma$ is sufficiently smooth. We prove that, if $q\in \Gamma$…

Using quadratic forms, we stablish a criteria to relate the curvature of a Riemannian manifold and partial hyperbolicity of its geodesic flow. We show some examples which satisfy the criteria and another which does not satisfy it but still…

In this paper, we show that starting from a geodesic ball $\overline{B_{r_0}}(0)$ in $\mathbb{H}^n$, for $n\geq3$, with prescribed non-decreasing rotationally symmetric mean curvature and the fixed conformal class $[g_{\mathbb{S}^{n-1}}]$…

We show geodesic completeness of certain compact locally symmetric pseudo-Riemannian manifolds of signature $(2,n)$. Our model space $\mathbf{X}$ is a $1$-connected, indecomposable symmetric space of signature $(2,n)$, that admits a unique…