Related papers: A local Lorentzian Ferrand-Obata theorem for confo…
In this paper we prove that the set of metrics conformal to the standard metric on $\mathbb{S}^{n}\backslash\{p_{1},\cdots,p_{l}\}$ is locally compact in $C^{m,\alpha}$ topology for any $m>0$, whenever the metrics have constant $\sigma_{k}$…
The non-existence of non-trivial conformally symmetric manifolds in the three-dimensional Riemannian setting is shown. In Lorentzian signature, a complete local classification is obtained. Furthermore, the isometry classes are examined.
We introduce a notion of uniform convergence for local and nonlocal curvatures. Then, we propose an abstract method to prove the convergence of the corresponding geometric flows, within the level set formulation. We apply such a general…
We consider smooth area-preserving flows (also known as locally Hamiltonian flows) on surfaces of genus $g\geq 1$ and study ergodic integrals of smooth observables along the flow trajectories. We show that these integrals display a…
We present a systematic study of causality theory on Lorentzian manifolds with continuous metrics. Examples are given which show that some standard facts in smooth Lorentzian geometry, such as light-cones being hypersurfaces, are wrong when…
We study the gradient flow of the length functional on the space of planar immersed closed curves, where the gradient is taken with respect to a family of homogeneous Sobolev $H^1$-type Riemannian metrics depending on parameters $\lambda>0$…
We give a new proof of the uniformization theorem of the leaves of a lamination by surfaces of hyperbolic conformal type. We use a laminated version of the Ricci flow to prove the existence of a laminated Riemannian metric (smooth on the…
Logarithmic conformal field theories are based on vertex algebras with non-semisimple representation categories. While examples of such theories have been known for more than 25 years, some crucial aspects of local logarithmic CFTs have…
We have shown that a particular class of non-local free field theory has conformal symmetry in arbitrary dimensions. Using the local field theory counterpart of this class, we have found the Noether currents and Ward identities of the…
We study conformal Fefferman-Lorentz manifolds introduced by Fefferman. To do so, we introduce Fefferman-Lorentz structure on (2n+2)-dimensional manifolds. By using causal conformal vector fields preserving that structure, we shall…
We show that any $k$ Osserman Lorentzian algebraic curvature tensor has constant sectional curvature and give an elementary proof that any local 2 point homogeneous Lorentzian manifold has constant sectional curvature. We also show that a…
The general form of a 2D conformal field theory (CFT) correlator on a Euclidean Riemann surface, Lorentzian plane or Lorentzian cylinder is well-known. This paper describes the general form of 2- and 3-point CFT correlators on the…
It is well-known that the flows generated by two smooth vector fields commute, if the Lie bracket of these vector fields vanishes. This assertion is known to extend to Lipschitz continuous vector fields, up to interpreting the vanishing of…
In this article, we study a locally constrained fully nonlinear curvature flow for convex capillary hypersurfaces in half-space. We prove that the flow preserves the convexity, exists for all time, and converges smoothly to a spherical cap.…
A locally metric connection on a smooth manifold $M$ is a torsion-free connection $D$ on $TM$ with compact restricted holonomy group $\mathrm{Hol}_0(D)$. If the holonomy representation of such a connection is irreducible, then $D$ preserves…
We investigate the formation of singularities in a self-similar form of regular solutions of the Localized Induction Approximation (also referred as to the binormal flow). This equation appears as an approximation model for the self-induced…
Minding's most celebrated result is his namesake theorem of 1839 which established that all surfaces having the same constant curvature must be locally isometric. Today, Minding's theorem is a staple in differential geometry textbooks. But,…
A conjecture of Hirschowitz's predicts that a globally generated vector bundle $W$ on a compact complex manifold $A$ satisfies the formal principle, i.e., the formal neighborhood of its zero section determines the germ of neighborhoods in…
We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut theorem for boundary regions, applied recently to develop a "bit-thread" interpretation of…
We show that any open set that is a finite distance away from a Lipschitz subgraph will become a Lipschitz subgraph after flowing under fractional mean curvature flow for a finite, universal time. Our proof is quantitative and inherently…