Geometrically infinite Kleinian groups have non-conical limit sets with the cardinality of the continuum. In this paper, we construct a geometrically infinite Fuchsian group such that the Hausdorff dimension of the non-conical limit set equals zero. For finitely generated, geometrically infinite Kleinian groups, we prove that the Hausdorff dimensio...
We describe the geometry of generic heterotic backgrounds preserving minimal supersymmetry in four dimensions using the language of generalised geometry. They are characterised by an SU(3) × Spin(6 + n) structure within O(6, 6 + n) × ℝ+ generalised geometry. Supersymmetry of the background is encoded in the existence of an involutive subbundle of t...
We show that it is $\mathsf{NP}$-hard to approximate the hyperspherical radius of a triangulated manifold up to an almost-polynomial factor.
Published in Annales Henri Poincaré
We show that a stationary solution of the Einstein–Maxwell equations which is close to a non-degenerate Reissner–Nordström–de Sitter solution is in fact equal to a slowly rotating Kerr–Newman–de Sitter solution. The proof uses the nonlinear stability of the Kerr–Newman–de Sitter family of black holes with small angular momenta, recently established...
We prove a new off-diagonal asymptotic of the Bergman kernels associated to tensor powers of a positive line bundle on a compact Kähler manifold. We show that if the Kähler potential is real analytic, then the Bergman kernel accepts a complete asymptotic expansion in a neighborhood of the diagonal of shrinking size 1\14 These improve the earlier re...
In this paper, we establish a min-max theory for constructing minimal disks with free boundary in any closed Riemannian manifold. The main result is an effective version of the partial Morse theory for minimal disks with free boundary established by Fraser. Our theory also includes as a special case the min-max theory for Plateau problem of minimal...
Given a compact Sasakian manifold, we endow the space of the Sasakian potentials with an analogue of Mabuchi metric. We show that its metric completion is negatively curved in the sense of Alexandrov.
We develop a general framework for the description of anomalies using extended functorial field theories extending previous work by Freed and Monnier. In this framework, anomalies are described by invertible field theories in one dimension higher and anomalous field theories live on their boundaries. We provide precise mathematical definitions for ...
An idealized observer of an astronomical event is situated at future null infinity, where light rays emitted from the source approach. Mathematically, null infinity corresponds to the portion of the spacetime boundary defined by equivalence classes of null geodesics. But what can we observe at future null infinity? In the note, we start by reviewin...
