A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Extends Weyl geometry from conformal to Weyl manifolds using ambient metrics.
Jet isomorphism theorems for conformal geometry are discussed. A new proof of the jet isomorphism theorem for odd-dimensional conformal geometry is outlined, using an ambient realization of the conformal deformation complex. An infinite order ambient lift for conformal densities in the case in which harmonic extension …
The study examines Lipschitz normally embedded Hölder triangles in 4D space.
We give a geometric derivation of Branson's Q-curvature in terms of the ambient metric associated with conformal structures; it naturally follows from the ambient metric construction of conformally invariant operators and can be applied to a large class of invariant operators. This procedure can be also applied to CR g…
Classifies homogeneous hypersurfaces in specific 4D geometries.
We show that the properties of Lagrangian mean curvature flow are a special case of a more general phenomenon, concerning couplings between geometric flows of the ambient space and of totally real submanifolds. Both flows are driven by ambient Ricci curvature or, in the non-Kähler case, by its analogues. To this end we…
Study links between surface germs and knot theory in 4D.
Lightlike manifolds studied via Cartan geometries in Lorentz-Minkowski spacetime.
New method improves counterfactual distribution learning for high-dimensional outcomes.
The study examines evolving star-shaped hypersurfaces in hyperbolic spaces, influenced by ambient geometry.
In this paper we relate the Fefferman-Graham ambient metric construction for conformal manifolds to the approach to conformal geometry via the canonical Cartan connection. We show that from any ambient metric that satisfies a weakening of the usual normalisation condition, one can construct the conformal standard tract…
Study of surfaces in space forms using Lie sphere geometry.
Conformal geodesics are distinguished curves on a conformal manifold, loosely analogous to geodesics of Riemannian geometry. One definition of them is as solutions to a third order differential equation determined by the conformal structure. There is an alternative description via the tractor calculus. In this article …
We prove a persistence result for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. The bounded geometry of the ambient manifold is a crucial assumption in order to control the uniformity of all estimates throughout the proof.
In this paper we study a geometric configuration of submanifolds of arbitrary codimension in an ambient Riemannian space. We obtain relations between the geometry of a q-codimension submanifold Mn along its boundary and the geometry of the boundary of Mn as an hypersuface of a q-codimensional submanifold Pn in an ambie…
The paper characterizes ambient metrics using conformal completion and null infinity properties.
The conformal Fefferman-Graham ambient metric construction is one of the most fundamental constructions in conformal geometry. It embeds a manifold with a conformal structure into a pseudo-Riemannian manifold whose Ricci tensor vanishes up to a certain order along the original manifold. Despite the general existence re…
Generative models use Riemannian manifolds to improve latent space interpretation.
Study recovers Riemannian quantities from noisy data densities.
High-dimensional models trained on smooth manifolds achieve optimal rates in Wasserstein metrics.
In this paper we consider surfaces which are critical points of the Willmore functional subject to constrained area. In the case of small area we calculate the corrections to the intrinsic geometry induced by the ambient curvature. These estimates together with the choice of an adapted geometric center of mass lead to …
Survey of mass partition problems in geometry and topology.
In his 1910 "Five Variables" paper, Cartan solved the equivalence problem for the geometry of distributions and in doing so demonstrated an intimate link between this geometry and the exceptional simple Lie groups of type . He claimed to produce a local classification of all such (complex) dis…
A new approach to Riemannian geometry using embedded and submersion structures.
Study on null hypersurfaces in complex contact manifolds.
We prove that the displacement energy of a stable coisotropic submanifold is bounded away from zero if the ambient symplectic manifold is closed, rational and satisfies a mild topological condition.
New method creates minimal submanifolds using complex-valued eigenfunctions.
Geometry-aware noise improves model generalization on complex manifolds.
Symmetry-breaking in three differential geometry conjectures.
CoreFlow models matrix-valued distributions efficiently, preserving shared low-rank structure.
We show that mean curvature flow of a compact submanifold in a complete Riemannian manifold cannot form singularity at time infinity if the ambient Riemannian manifold has bounded geometry and satisfies certain curvature and volume growth conditions .
Tractor Calculus is a powerful tool for analyzing Weyl invariance; although fundamentally linked to the Cartan connection, it may also be arrived at geometrically by viewing a conformal manifold as the space of null rays in a Lorentzian ambient space. For dimension d conformally flat manifolds we show that the (d+2)-di…
Study of weighted nonlinear flags in symplectic geometry.
A contact projective structure is a contact path geometry the paths of which are among the geodesics of some affine connection. In the manner of T.Y. Thomas there is associated to each contact projective structure an ambient affine connection on a symplectic manifold with one-dimensional fibers over the contact manifol…
Extends mean curvature to surfaces in Riemann-Cartan geometry with torsion.
Researchers create new operators from Riemannian invariants.
The paper classifies degenerate almost complex surfaces in a nearly Kähler space.
For Hitchin's generalised geometries we introduce and analyse the concept of a structured submanifold which encapsulates the classical notion of a calibrated submanifold. Under a suitable integrability condition on the ambient geometry, these generalised calibrated cycles minimise a functional occurring as D-brane ener…
Modern sample points in many applications no longer comprise real vectors in a real vector space but sample points of much more complex structures, which may be represented as points in a space with a certain underlying geometric structure, namely a manifold. Manifold learning is an emerging field for learning the unde…
Introduces quadratic linking degree in algebraic geometry.
The paper explores projective structures on curves and their applications in conformal geometry.
We prove differential Harnack inequalities for flows of strictly convex hypersurfaces by powers , , of the mean curvature in Einstein manifolds with a positive lower bound on the sectional curvature. We assume that this lower bound is sufficiently large compared to the derivatives of the curvature tensor of t…
Polynomial error equidistribution for SL2 groups.
We produce examples of codimension one foliations of the Euclidean and hyperbolic planes with bounded geometry which are topologically products, but for which leaves are non-recursively distorted. That is, the function which compares intrinsic distances in leaves with extrinsic distances in the ambient space grows fast…
Latent variable models (LVMs) learn probabilistic models of data manifolds lying in an \emph{ambient} Euclidean space. In a number of applications, a priori known spatial constraints can shrink the ambient space into a considerably smaller manifold. Additionally, in these applications the Euclidean geometry might induc…
We introduce a class of null hypersurfaces of a semi-Riemannian manifold, namely, screen quasi-conformal hypersurfaces, whose geometry may be studied through the geometry of its screen distribution. In particular, this notion allows us to extend some results of previous works to the case in which the sectional curvatur…
We prove a persistence result for noncompact normally hyperbolic invariant manifolds in the setting of Riemannian manifolds of bounded geometry. Bounded geometry of the ambient manifold is a crucial assumption required to control the uniformity of all estimates throughout the proof. The -smoothness result is o…
We study the uniqueness of minimal submanifolds and the stability of the mean curvature flow in several well-known model spaces of manifolds of special holonomy. These include the Stenzel metric on the cotangent bundle of spheres, the Calabi metric on the cotangent bundle of complex projective spaces, and the Bryant--S…