Related papers: Locally Lipschitz graph property for lines
We study algebraic isomonodromic deformations of flat logarithmic connections on the Riemann sphere with $n\geq 4$ poles, for arbitrary rank. We introduce a natural property of algebraizability for the germ of universal deformation of such…
Liv\v{s}ic theorem for flows asserts that a Lipschitz observable that has zero mean average along every periodic orbit is necessarily a coboundary, that is the Lie derivative of a Lipschitz function smooth along the flow direction. The…
We prove several results for the Dirichlet, Neumann and Regularity problems for the Laplace equation in graph Lipschitz domains in the plane, considering $A_{\infty}$-measures on the boundary. More specifically, we study the…
We study connected components of the Morse boundary and their stabilisers. We introduce the notion of point-convergence and show that if the set of non-singleton connected components of the Morse boundary of a finitely generated group $G$…
We investigate the spectra of a family of pairs (M_i,A_i) consisting of a complete Riemannian manifold M_i and a closed subset A_i and which converge in the Lipschitz topology to a pair (M,A). This is used to construct manifolds of bounded…
We study conditions under which a piecewise affine mapping has the Lipschitz shadowing property. As an application, we show that there exists a homeomorphism with a nonisolated fixed point having the Lipschitz shadowing property.
We give an upper bound on the number of perfect matchings in an undirected simple graph $G$ with an even number of vertices, in terms of the degrees of all the vertices in $G$. This bound is sharp if $G$ is a union of complete bipartite…
Let ${\cal M}_{t,v,r}(n,m)$, $2\leq m<n$, be the collection of self-affine carpets with expanding matrix $\diag(n,m)$ which are totally disconnected, possessing vacant rows and with uniform horizontal fibers. In this paper, we introduce a…
For some class of mappings, there are investigated problems connected with a possibility of continuous extension to a boundary on Riemannian manifolds. In particular, for so-called ring mappings, there is proved a result related to…
A digraph is connected-homogeneous if any isomorphism between finite connected induced subdigraphs extends to an automorphism of the digraph. We consider locally-finite connected-homogeneous digraphs with more than one end. In the case that…
In this paper we prove local interior and boundary Lipschitz continuity of solutions of a free boundary problem involving the $A$-Laplacian. We also show that the free boundary is represented locally by graphs of a family of lower…
We generalize Siegel's theorem on integral points on affine curves to integral points of bounded degree, giving a complete characterization of affine curves with infinitely many integral points of degree d or less over some number field.…
Steinerberger defined a notion of boundary for a graph and established a corresponding isoperimetric inquality. Hence, "large" graphs have more boundary vertices. In this paper, we first characterize graphs with three boundary vertices in…
For a compact connected Riemannian manifold with smooth boundary, by computing the full symbol of the elastic Dirichlet-to-Neumann map, we prove that the elastic Dirichlet-to-Neumann map can uniquely determine the partial derivatives of all…
In this paper, we study capillary graphs defined on a domain $\Omega$ of a complete Riemannian manifold $M$, where a graph is said to be capillary if it has constant mean curvature and locally constant Dirichlet and Neumann conditions on…
We prove that the presence or absence of corners is spectrally determined in the following sense: any simply connected domain with piecewise smooth Lipschitz boundary cannot be isospectral to any connected domain, of any genus, which has…
We review the notion of (finitary) filter pair as a tool for creating and analyzing logics. A filter pair can be seen as a presentation of a logic, given by presenting its lattice of theories as the image of a lattice homomorphism, with…
Stationary geodesic networks are the analogs of closed geodesics whose domain is a graph instead of a circle. We prove that for a Baire-generic Riemannian metric on a smooth manifold $M$, all connected embedded stationary geodesic nets are…
Laplacian operators on finite compact metric graphs are considered under the assumption that matching conditions at graph vertices are of $\delta$ and $\delta'$ types. An infinite series of trace formulae is obtained which link together two…
We determine when a quasi-isometry between discrete spaces is at bounded distance from a bilipschitz map. From this we prove a geometric version of the Von Neumann conjecture on amenability. We also get some examples in geometric groups…