Related papers: On differentiable compactifications of the hyperbo…
We find a compactification of the $\mathrm{SO}_{0}(2,3)$-Hitchin component by studying the degeneration of the induced metric on the unique equivariant maximal surface in the 4-dimensional pseudo-hyperbolic space $\mathbb{H}^{2,2}$. In the…
We study the isometry group of a globally hyperbolic spatially compact Lorentz surface. Such a group acts on the circle, and we show that when the isometry group acts non properly, the subgroups of $\mathrm{Diff}(\mathbb{S}^1)$ obtained are…
The construction of superintegrable systems based on Lie algebras and their universal enveloping algebras has been widely studied over the past decades. However, most constructions rely on explicit differential operator realisations and…
In this paper we generalize work of Amice and Lazard from the early (nineteen) sixties. Amice determined the dual of the space of locally Qp-analytic functions on Zp and showed that it is isomorphic to the ring of rigid functions on the…
We establish rigidity for partial transformation groupoids associated with algebraic actions of semigroups: If two such groupoids (satisfying appropriate conditions) are isomorphic, then the globalizations of the initial algebraic actions…
Algebraic hypergeometric functions can be compactly expressed as radical functions on pull-back curves where the monodromy group is simpler, say, a finite cyclic group. These so-called Darboux evaluations were already considered for…
This article generalizes the result of Katzarkov and Ramachandran from algebraic surfaces to K\"ahler surfaces. We follow their argument to prove the holomorphic convexity of a reductive Galois covering over a compact K\"ahler surface which…
Given a discrete quantum group A we construct a certain Hopf *-algebra AP which is a unital *-subalgebra of the multiplier algebra of A. The structure maps for AP are inherited from M(A) and thus the construction yields a compactification…
Given a compact, connected Lie group $K$, we use principal $K$-bundles to construct manifolds with prescribed finite-dimensional algebraic models. Conversely, let $M$ be a compact, connected, smooth manifold which supports an almost free…
We show that for any closed surface of genus greater than one and for any finite weighted graph filling the surface, there exists a hyperbolic metric which realizes the least Dirichlet energy harmonic embedding of the graph among a fixed…
When considered as a Deligne-Lusztig variety, the Drinfeld half space $\Omega_V$ over a finite field $k$ has a compactification whose boundary divisor is normal crossing and which can be obtained by successively blowing-up projective space…
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…
This paper unites the gauge-theoretic and hyperbolic-geometric perspectives on the asymptotic geometry of the character variety of SL(2,C) representations of a surface group. Specifically, we find an asymptotic correspondence between the…
The main result of this paper is the conformal flatness of real-analytic compact Lorentz manifolds of dimension at least $3$ admitting a conformal essential (i.e. conformal, but not isometric) action of a Lie group locally isomorphic to…
In this paper, we construct a geometrical compactification of the geodesic flow of non-compact complete hyperbolic surfaces $\Sigma$ without cusps having finitely generated fundamental group. We study the dynamical properties of the…
The volume cut off by a hyperplane from a bounded body with smooth boundary in $R^{2k}$ never is an algebraic function on the space of hyperplanes: for k=1 it is the famous lemma XXVIII from Newton's Principia. Following an analogy of these…
We describe a compactification by KSBA stable pairs of the five-dimensional moduli space of K3 surfaces with purely non-symplectic automorphism of order four and $U(2)\oplus D_4^{\oplus2}$ lattice polarization. These K3 surfaces can be…
We consider a description of lattice gravity in six dimensions, where the two extra dimensions have been compactified on a warped hyperbolic disk of constant curvature. We analyze a fine-grained latticization of the hyperbolic disk in the…
We show that a class of algebras is closed under the taking of homomorphic images and direct products if and only if the class consists of all algebras that satisfy a set of (generally simultaneous) equations. For classes of regular…
We construct a compactification of the moduli spaces of abelian differentials on Riemann surfaces with prescribed zeroes and poles. This compactification, called the moduli space of multi-scale differentials, is a complex orbifold with…