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.
Proves existence and uniqueness of weighted metrics for smooth spaces.
New property: polygons have a fixed dimension regardless of ambient space dimensions.
For a conformal manifold we introduce the notion of an ambient connection, an affine connection on an ambient manifold of the conformal manifold, possibly with torsion, and with conditions relating it to the conformal structure. The purpose of this construction is to realise the normal conformal tractor holonomy as aff…
It is shown that any transverse invariant measure of a foliated space can be considered as a measure on the ambient space.
We prove existence and uniqueness of weighted ambient metric for manifolds with density.
Generative models use Riemannian manifolds to improve latent space interpretation.
Extends submanifold theorem to general spaces.
Generative adversarial models are powerful tools to model structure in complex distributions for a variety of tasks. Current techniques for learning generative models require an access to samples which have high quality, and advanced generative models are applied to generate samples from noisy training data through amb…
We study deformations of free boundary constant mean curvature (CMC) hypersurfaces whose Jacobi operator is degenerate due to symmetries of the ambient space. The value of the mean curvature and the ambient metric are allowed to vary simultaneously, provided that the infinitesimal ambient symmetries change smoothly. We…
We give simple conditions on an ambient manifold that are necessary and sufficient for isoperimetric inequalities (for submanifolds) to hold.
Researchers create a family of conformally covariant operators.
Extends Weyl geometry from conformal to Weyl manifolds using ambient metrics.
Avoids noncompact hypersurfaces from touching in evolving flows.
New method uses Diffusion Maps for latent space modeling of dynamical systems.
We present conformal structures in signature (3,2) for which the holonomy of the Fefferman-Graham ambient metric is equal to the non-compact exceptional Lie group G_{2(2)}. We write down the resulting 8-parameter family of G_{2(2)}-metrics in dimension seven explicitly in an appropriately chosen coordinate system on th…
The study examines evolving star-shaped hypersurfaces in hyperbolic spaces, influenced by ambient geometry.
We provide a self-contained treatment of set-theoretic subsolutions to flow by mean curvature, or, more generally, to flow by mean curvature plus an ambient vector field. The ambient space can be any smooth Riemannian manifold. Most importantly, we show that if two such set-theoretic subsolutions are initially disjoint…
The paper proves rigidity for shells in non-Euclidean spaces.
We study piecewise linear co-dimension two embeddings of closed oriented manifolds in Euclidean space, and show that any such embedding can always be isotoped to be a closed braid as long as the ambient dimension is at most five, extending results of Alexander (in ambient dimension three), and Viro and independently Ka…
Study recovers Riemannian quantities from noisy data densities.
Examines discrete curvature's relation to smooth curvature in 3 spaces.
We study rays and co-rays in the Wasserstein space () whose ambient space is a complete, separable, non-compact, locally compact length space. We show that rays in the Wasserstein space can be represented as probability measures concentrated on the set of rays in the ambient spac…
The study examines Lipschitz normally embedded Hölder triangles in 4D space.
Estimates area and spectrum of stable minimal surfaces in Euclidean and hyperbolic spaces.
In the article, we generalize some recent results of Colding and Minicozzi on generic singularities of mean curvature flow to curved ambient spaces. To do so, we make use of a weighted monotonicity formula to derive an "almost monotonicity" for the entropy upon embedding into . We are also lead to study the co…
In this paper we will prove Hadamard-Stoker type theorems in the following ambient spaces: $\man ^n \times \r$, where $\man ^n $ is a pinched manifold, and certain Killing submersions, e.g., Berger spheres and Heisenberg spaces. That is, under the condition that the principal curvatures of an immersed hypersurfac…
Study area-minimizing hypersurfaces in singular manifolds with nonnegative scalar curvature.
Study of surfaces in space forms using Lie sphere geometry.
The purpose of this article is to determine explicitly the complete surfaces with parallel mean curvature vector, both in the complex projective plane and the complex hyperbolic plane. The main results are as follows: When the curvature of the ambient space is positive, there exists a unique such surface up to rigid mo…
Paper proves existence of ambient manifolds for null hypersurfaces solving Einstein equations.
The paper embeds CR manifolds into twistor spaces and constructs neutral hyperkähler metrics.
Generalizes embedding formalism for CFTs on curved backgrounds.
It is well-known that for a surface in a 3-dimensional real space form the constancy of the mean curvature is equivalent to the harmonicity of the Gauss map. However, this is not true in general for surfaces in an arbitrary 3-dimensional ambient space. In this paper we study this problem for surfaces in an important an…
In this article we study complex properties of minimal Lagrangian submanifolds in Kaehler ambient spaces, and how they depend on the ambient curvature. In particular, we prove that, in the negative curvature case, minimal Lagrangians do not admit fillings by holomorphic discs. The proof relies on a mix of holomorphic c…
In this paper we prove that stable, compact without boundary, oriented, nonzero constant mean curvature surfaces in the de Sitter-Schwarzschild and Reissner-Nordstrom manifolds are the slices, provided its mean curvature satisfies some positive lower bound. More generally, we prove that stable, compact without boundary…
We show some computations related to the motion by mean curvature flow of a submanifold inside an ambient Riemannian manifold evolving by Ricci or backward Ricci flow. Special emphasis is given to the possible generalization of Huisken's monotonicity formula and its connection with the validity of some Li--Yau--Hamilto…
New research shows that the dimension gap between intrinsic and ambient dimensions affects adversarial vulnerability of machine learning models.
This paper constructs a family of conformally invariant differential operators acting on spinor densities with leading part a power of the Dirac operator. The construction applies for all powers in odd dimensions, and only for finitely many powers in even dimensions. These operators arise naturally as obstructions to f…
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…
Study shows how certain hypersurfaces evolve under mean curvature flow.
Given any two Einstein (pseudo-)metrics, with scalar curvatures suitably related, we give an explicit construction of a Poincaré-Einstein (pseudo-)metric with conformal infinity the conformal class of the product of the initial metrics. We show that these metrics are equivalent to ambient metrics for the given conforma…
Study limits of Kähler submanifolds and prove no holomorphic isometries.
Researchers describe a specific type of submanifolds in Euclidean space.
New technique identifies submanifolds in symmetric spaces based on Ricci curvature.
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…
Curvature of 2D subsets preserved in their space.
Often noisy point clouds are given as an approximation of a particular compact set of interest. A finite point cloud is a compact set. This paper proves a reconstruction theorem which gives a sufficient condition, as a bound on the Hausdorff distance between two compact sets, for when certain offsets of these two sets …
Study of elastic models in non-Euclidean spaces via Γ-convergence.