Related papers: Holomorphic horospherical duality "sphere-cone"

We present a construction for the holomorph of an inverse semigroup, derived from the cartesian closed structure of the category of ordered groupoids. We compare the holomorph with the monoid of mappings that preserve the ternary heap…

Recently it has been speculated that a set of diffeomorphisms exist which act non-trivially on the horizon of some black holes such as Kerr and Kerr-Newman black hole. %\cite{Haco:2018ske,Haco:2019ggi}. Using this symmetry in covariant…

Complex manifolds with compatible metric have a naturally defined subspace of harmonic differential forms that satisfy Serre, Hodge, and conjugation duality, as well as hard Lefschetz duality. This last property follows from a…

We present some addition theorems for spin-weighted spherical harmonics, generalizing previous results for scalar (spin-zero) spherical harmonics. These addition theorems involve sums over the azimuthal quantum number of products of two…

We study the interplay between the classical theory of linear series on curves, and the recent theory of linear series on graphs. We prove that every d-gonal (weighted) graph of Hurwitz type is the dual graph of a d-gonal curve. Conversely…

Finite-energy topological spherically symmetrical solutions of Chiral Born-Infeld Theory are studied. Properties of these solution are obtained, and a possible physical interpretation is also given.

This article is a survey about or introduction to certain aspects of the complex geometry of a hypothetical complex structure on the six-sphere. We discuss a result of Peternell--Campana--Demailly on the algebraic dimension of a…

Locally harmonic manifolds are Riemannian manifolds in which small geodesic spheres are isoparametric hypersurfaces, i.e., hypersurfaces whose nearby parallel hypersurfaces are of constant mean curvature. Flat and rank one symmetric spaces…

A hyperbolic algebraic curve is a bounded subset of an algebraic set. We study the function theory and functional analytic aspects of these sets. We show that their function theory can be described by finite codimensional subalgebras of the…

We study a geometric notion related to formality for Bott-Chern cohomology on complex manifolds.

We advocate an account of dualities between physical theories: the basic idea is that dual theories are isomorphic representations of a common core. We defend and illustrate this account, which we call a Schema, in relation to symmetries.…

A conformal map from a Riemann surface to a Euclidean space of dimension greater than or equal to three is explained by using the Clifford algebra, in a similar fashion to quaternionic holomorphic geometry of surfaces in the Euclidean…

We establish a general result on the existence of partially defined semiconjugacies between rational functions acting on the Riemann sphere. The semiconjugacies are defined on the complements to at most one-dimensional sets. They are…

A topological shape analysis is proposed and utilized to learn concepts that reflect shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects. Therein constellations…

We investigate the geometry of holomorphic curves and complex surfaces from the perspective of singularity theory. We show that, with a suitable choice of a complex bilinear symmetric form, the families of functions and mappings that…

We consider stable manifolds of a holomorphic diffeomorphism of a complex manifold. Using a conjugation of the dynamics to a (non-stationary) polynomial normal form, we show that typical stable manifolds are biholomorphic to complex…

We classify all edge-to-edge spherical isohedral 4-gonal tilings such that the skeletons are pseudo-double wheels. For this, we characterize these spherical tilings by a quadratic equation for the cosine of an edge-length. By the…

We provide first a categorical exploration of, and then completion of the mapping of the relationships among, three fundamental perspectives on binary relations: as the incidence matrices of hypergraphs, as the formal contexts of concept…

We derive a holographic relation for the dS static patch with the dual field theory defined on the observer horizon. The starting point is the duality of higher-spin theory on AdS_4 and the O(N) vector model. We build on a similar analytic…

We consider the complexification of the Henon family of quadratic diffeomorphisms of the plane, and the region of parameter space corresponding to complex horseshoes. We discuss some conjectures about the global topology of the complex…