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 studies curvature changes on manifolds with boundary.
Study on deformations of special Lagrangians with boundary in Calabi-Yau manifolds.
Study on deforming calibrated submanifolds with boundary constraints.
Develops a method to deform metrics on manifolds with non-compact boundaries.
Proof of theorem for 7D manifolds with boundary using Witten deformation.
The paper explores how to increase Steklov spectral gaps on manifolds with fixed boundary.
Developing deformation theory for Calabi-Yau 3-folds with boundary.
A behavior of extreme networks under deformations of their boundary sets is investigated. It is shown that analyticity of a deformation of boundary set guarantees preservation of the networks types for minimal spanning trees, minimal fillings and so-called stable shortest trees in the Euclidean space.
We introduce a deformation of Riemann surfaces and we are interested in the convergence of this deformation to a point of the Gardiner-masur boundary of Teichmueller space. This deformation, which we call the horocyclic deformation, is directed by a projective measured foliation and belongs to a certain horocycle in a …
Study on deforming discrete conformal structures on surfaces with boundaries.
New index formulae derived for operators on boundary groupoids.
Localized deformation of scalar curvature and mean curvature on manifolds.
The paper solves scalar curvature problems under conformal deformation for Riemannian manifolds.
Author reduces the Minkowski problem to the problem of construction the G-deformations preserving the product of principal curvatures for every point of surface in Riemannian space. G-deformation transfers every normal vector of surface in parallel along the path of the translation for each point of surface. The contin…
On a manifold with boundary, we deform the metric conformally. This induces a deformation of the Schouten tensor. We fix the metric at the boundary and realize a prescribed value for the product of the eigenvalues of the Schouten tensor in the interior, provided that there exists a subsolution.
Constructs obstructions and deformation principles for positive scalar curvature metrics with mean convex boundaries.
We consider natural conformal invariants arising from the Gauss-Bonnet formulas on manifolds with boundary, and study conformal deformation problems associated to them. The key technique we used is to derive boundary C^2 estimates directly from C^0 estimates for fully nonlinear equations. The main result has appeared i…
Researchers find multiple ways to deform manifolds with specific curvature properties.
Boundary value problems for operators of Dirac type arise naturally in connection with the conformal geometry of surfaces immersed in Euclidean 3--space. Recently such boundary value problems have been successfully applied to a variety of problems from computer graphics. Here we investigate under which conditions these…
Elliptic boundary value problem for G2 structures on manifolds.
Let M be a complete finite-volume hyperbolic 3-manifold with compact non-empty geodesic boundary and k toric cusps, and let T be a geometric partially truncated triangulation of M. We show that the variety of solutions of consistency equations for T is a smooth manifold or real dimension 2k near the point representing …
Computes spectral Einstein functional for Witten deformation on even-dimensional spin manifolds.
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…
Coassociative 4-folds are a particular class of 4-dimensional submanifolds which are defined in a 7-dimensional manifold M with a G_2 structure given by a `positive' differential 3-form, sometimes called G_2-form. Assuming that a G_2-form on M is closed, we study deformations of a compact coassociative submanifold N wi…
Locally connected deformation spaces for 3-manifolds.
Given an ideal triangulation of a connected 3-manifold with non-empty boundary consisting of a disjoint union of tori, a point of the deformation variety is an assignment of complex numbers to the dihedral angles of the tetrahedra subject to Thurston's gluing equations. From this, one can recover a representation of th…
Symplectic coordinates found on projective structures on orbifolds.
Let M be an 8-manifold with a Spin(7)-structure. We first show that closed Cayley submanifolds of M form a smooth moduli space for a generic Spin(7)-structure. Then we study the deformations of a compact, connected Cayley submanifold X of M with non-empty boundary contained in a given submanifold W of M such that X and…
Let be a special Lagrangian submanifold of a compact, Calabi-Yau manifold with boundary lying on the symplectic, codimension 2 submanifold . It is shown how deformations of which keep the boundary of confined to can be described by an elliptic boundary value problem, and two results about minimal…
Study on ALH manifolds with boundary, showing surjectivity of scalar curvature map and mass rigidity.
Paper extends noncompact Llarull's theorem to manifolds with boundary.
The paper proves formulas and theorems for J-Witten deformation on specific manifolds.
Study on metrics with positive scalar curvature and convex boundary.
Novel boundary conditions for Ricci flow to deform compact manifolds.
The paper studies topological indices of geometric operators on manifolds with fibered boundaries.
We derive an identity for Margulis invariants of affine deformations of a complete orientable one-ended hyperbolic sur- face following the identities of McShane, Mirzakhani and Tan- Wong-Zhang. As a corollary, a deformation of the surface which infinitesimally lengthens all interior simple closed curves must in- finite…
Study the boundary of a space related to Outer space.
Let X be a compact 4-manifold with boundary. We study the space of hyperkähler triples on X, modulo diffeomorphisms which are the identity on the boundary. We prove that this moduli space is a smooth infinite-dimensional manifold and describe the tangent space in terms of triples of closed anti-self-dual 2-forms. We al…
Formula calculates index for CR operators on surfaces with boundary punctures.
We describe a simple fundamental domain for the holonomy group of the boundary unipotent spherical CR uniformization of the figure eight knot complement, and deduce that small deformations of that holonomy group (such that the boundary holonomy remains parabolic) also give a uniformization of the figure eight knot comp…
Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define motions and conformal motions together with deformational decomposition of manifol…
Maximal cusps are not dense on Teichmüller space for infinite-type surfaces.
We describe the deformation space of a solid torus with boundary modelled on convex ideal hyperbolic polyhedra. This deformation space is given by natural Gauss--Bonnet type inequalities on the dihedral angles. The result extends to solid tori with an arbitrary conical singularity along the core. Our method is to decom…
Proves existence and uniqueness of weak solutions for specific equations.
The paper studies how Kleinian groups can be deformed while preserving their peripheral structures.
The study finds multiple solutions to a complex metric problem using bifurcation theory.
Paper proves gluing formula for analytic torsions using Witten deformation for non-Morse functions.
We prove that the deformation space AH(M) of marked hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold M with incompressible boundary is locally connected at minimally parabolic points. Moreover, spaces of Kleinian surface groups are locally connected at quasiconformally rigid points. Similar resu…