Related papers: A Newman property for BLD-mappings

We say that a cover of surfaces S -> X has the Birman--Hilden property if the subgroup of the mapping class group of X consisting of mapping classes that have representatives that lift to S embeds in the mapping class group of S modulo the…

This is a survey on known results and open problems about Smooth and PL-Rigidity Problem for negatively curved locally symmetric spaces. We also review some developments about studying the basic topological properties of the space of…

We study a version of Calder\'on's problem for harmonic maps between Riemannian manifolds. By using the higher linearization method, we first show that the Dirichlet-to-Neumann map determines the metric on the domain up to a natural gauge…

We show that the co-rays to a ray in a complete non-compact Finsler manifold contain geodesic segments to upper level sets of Busemann functions. Moreover, we characterise the co-point set to a ray as the cut locus of such level sets. The…

We study boundary uniqueness properties of Hardy space functions in several complex variables. Along the way, we develop properties of the Lumer Hardy space.

We introduce a system of axioms that uniquely defines an (infinity,d)-category of bordisms equipped with geometric data. The underlying manifolds of these bordisms may be smooth, complex, super, or formal smooth manifolds, as well as any…

We study the properties of the set where a generalized function of bounded variation has infinite approximate limit, highlighting in this way the main geometric difference with functions of bounded variation. To this aim we prove a new…

Co lombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and exterior algebra are studied. A point value…

We prove estimates for eigenfunctions on a manifold equipped with a smooth metric. We use these estimates in order estimate the size of their nodal sets.

Certain curvature properties and scalar invariants of the manifolds belonging to one of the main classes almost contact manifolds with Norden metric are considered. An example illustrating the obtained results is given and studied.

Let B be the Bergman projection associated to a domain on which the dbar-Neumann operator is compact. We show that arbitrary L^2 derivatives of Bf are controlled by derivatives of f taken in a single, distinguished direction. As a…

Local properties of the fundamental group of a path-connected topological space can pose obstructions to the applicability of covering space theory. A generalized covering map is a generalization of the classical notion of covering map…

In this paper, invariant submanifolds of a generalized Kenmotsu manifold are studied. Necessary and sufficient conditions are given on a submanifold of a generalized Kenmotsu manifold to be an invariant submanifold.In this case, we…

We discuss geometric properties of covers of closed hyperbolic manifolds of dimension $n\geq 3$, branched along a totally geodesic codimension two submanifold $\Sigma$. The results are mostly known to the experts but hard to find in the…

We show that the holonomy invariance of a function on the tangent bundle of a manifold, together with very mild regularity conditions on the function, is equivalent to the existence of local parallelisms compatible with the function in a…

We propose a conjecture on integrality property of the open-closed mirror maps of compact Calabi-Yau manifolds. Some examples are presented.

We provide necessary and sufficient conditions for a set-valued mapping between finite dimensional spaces to be directionally open by relating this property with directional regularity, H\"older continuity of the inverse mapping,…

We study function spaces parametrized by neural networks, referred to as neuromanifolds. Specifically, we focus on deep Multi-Layer Perceptrons (MLPs) and Convolutional Neural Networks (CNNs) with an activation function that is a…

We take the fundamental group of the complement of the branch curve of a generic projection induced from canonical embedding of a surface. This group is stable on connected components of moduli spaces of surfaces. Since for many classes of…

The first part of this work constructs positive-genus real Gromov-Witten invariants of real-orientable symplectic manifolds of odd "complex" dimensions; the present part focuses on their properties that are essential for actually working…