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.
The paper proves a local existence theorem for a CR torsion flow in pseudohermitian manifolds.
Vaisman's theorem extended to locally reducible Kähler spaces.
Study local curvature estimates and existence of conformal metrics on noncompact manifolds.
In this paper we prove a new version of the Schoenflies extension theorem for collared domains in Euclidean n-space: for 1 < p < n, locally bi-Lipschitz homeomorphisms between collared domains with locally p-integrable, second-order weak derivatives admit homeomorphic extensions of the same regularity. Moreover, the th…
The Abstract Boundary singularity theorem was first proven by Ashley and Scott. It links the existence of incomplete causal geodesics in strongly causal, maximally extended spacetimes to the existence of Abstract Boundary essential singularities, i.e., non-removable singular boundary points. We give two generalizations…
Study generalizes map properties between Hermitian manifolds preserving specific forms.
In this paper, we give the first detailed proof of the short-time existence of Deane Yang's local Ricci flow. Then using the local Ricci flow, we prove short-time existence of the Ricci flow on noncompact manifolds, whose Ricci curvature has global lower bound and sectional curvature has only local average integral bou…
A theorem proves integrability of Fréchet tangent distributions.
Proves compactness of geometric models for certain homogeneous spaces.
New theorem on geodesics on non-compact manifolds.
We prove the existence of the flow by curvature of regular planar networks starting from an initial network which is non-regular. The proof relies on a monotonicity formula for expanding solutions and a local regularity result for the network flow in the spirit of B. White's local regularity theorem for mean curvature …
We give a new proof for the local existence of a smooth isometric embedding of a smooth -dimensional Riemannian manifold with nonzero Riemannian curvature tensor into -dimensional Euclidean space. Our proof avoids the sophisticated arguments via microlocal analysis used in earlier proofs. In Part 1, we introduce …
Recently, Cochran and Harvey defined torsion-free derived series of groups and proved an injectivity theorem on the associated torsion-free quotients. We show that there is a universal construction which extends such an injectivity theorem to an isomorphism theorem. Our result relates injectivity theorems to a certain …
Slice theorem in infinite dimensions for Lie groups.
The paper introduces a new concept of infinitesimal homogeneity for connections on bundles and applies it to prove known theorems and derive new results.
In this paper, we prove an existence theorem of a local moduli space for geometric structures in a very general setting. Then to show the interest of this result, we apply it to the case of sasakian and Sasaki-Einstein structures.
The paper proves local isometric embeddings for singular metrics near a point.
Localized min-max method proves minimal hypersurface existence.
Extends Whitney's theorem for functions on rough boundaries.
The study proves local rigidity of minimal 2-spheres in electrovacuum spacetimes.
Universal functions and metrics with constant curvature on domains.
Taking an elementary and straightforward approach, we develop the concept of a regular value for a smooth map f: O -> P between smooth orbifolds O and P. We show that Sard's theorem holds and that the inverse image of a regular value is a smooth full suborbifold of O. We also study some constraints that the existence o…
Paper proves mass theorems for nonnegative scalar curvature metrics.
We present an elementary treatment of the Optional Decomposition Theorem for continuous semimartingales and general filtrations. This treatment does not assume the existence of equivalent local martingale measure(s), only that of strictly positive local martingale deflator(s).
Proves a synthetic Lorentzian Cartan-Hadamard theorem.
Kuranishi's proof of complex deformation theory revisited
Study non-Kahler symplectic manifolds, proving deformation and Torelli theorems.
Quantum codes with optimal distance and dimension for n-dimensional space.
New proof of link factorization theorem, avoiding case exhaustion.
The study finds static solutions in symplectic curvature flow in 4D.
The author presents the generalized Stokes theorem for R-linear forms on Lie algebroids (which can be non-local). We apply the Stokes formula on forms to prove that two homotopic homomorphisms of Lie algebroids implies the existence of a chain operator joining their pullback operators.
A locally conformally symplectic (LCS) form is an almost symplectic form such that a closed one-form exists with . We present a version of the well-known result of Darboux and Weinstein in the LCS setting and give an application concerning Lagrangian submanifolds.
Proves a local analytic Bertini theorem confirming a conjecture.
The classical Sturm-Hurwitz-Kellogg theorem asserts that a function, orthogonal to an n-dimensional Chebyshev system on a circle, has at least n+1 sign changes. We prove the converse: given an n-dimensional Chebyshev system on a circle and a function with at least n+1 sign changes, there exists an orientation preservin…
Survey discusses recent advances on Brakke flows and their properties.
We prove an existence theorem for Spin(7)-instantons, which are highly concentrated near a Cayley submanifold; thus giving a partial converse to Tian's foundational compactness theorem. As an application, we show how to construct Spin(7)-instantons on Spin(7)-manifolds with suitable local K3 Cayley fibrations. This rec…
The paper proves a unique conformal measure for Anosov groups and shows local mixing.
Article strengthens initial data rigidity theorem to show unique spacetime extension.
Paper proves a Cohen-Dimca-Orlik type theorem for Z-local systems of hyperplane arrangements.
In his monograph "Leçons sur les systèmes orthogonaux et les coordonnées curvilignes. Principes de géométrie analytique", 1910, Darboux stated three theorems providing local existence and uniqueness of solutions to first order systems of the type \[\partial_{x_i} u_α(x)=f^α_i(x,u(x)),\quad i\in I_α\subseteq\{1,\dots,n\…
In this paper, we introduce new methods for solving the vacuum Einstein constraints equations: the first one is based on Schaefer's fixed point theorem (known methods use Schauder's fixed point theorem) while the second one uses the concept of half-continuity coupled with the introduction of local supersolutions. These…
Enhances Ricci flow theorem with scalar curvature bound.
We generalize classical theorems due to Lichnerowicz and Hitchin on the existence of Riemannian metrics of positive scalar curvature on spin manifolds to the case of foliated spin manifolds. As a consequence, we show that there is no foliation of positive leafwise scalar curvature on any torus, which generalizes the fa…
The goal of the present paper is to establish some kind of regularity of an energy minimizer map between Riemannian polyhedra. More precisely, we will show the hölder continuity of local energy minimizers between Riemannian polyhedra with the target spaces without focal points. With this new result, we also complete ou…
The abstract proves the existence and regularity of Brakke flows starting from a given set.
New method proves Alexandrov theorem for curved spacetimes.
Proves a local version of Myers-Steenrod theorem for specific manifolds.
Paper extends Poincaré's work to stochastic differential equations.