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.
Study of combinatorial Calabi flow on ideal circle patterns.
Paper solves long-standing problem of infinite ideal polyhedra in hyperbolic space.
New method finds ideal circle patterns on spheres.
The flow converges without Kähler-Einstein and develops ideal sheaves.
New method simplifies ideal curve flow with length constraint.
New jellyfish found in various flows.
Given a general pseudo-Anosov flow in a three manifold, the orbit space of the lifted flow to the universal cover is homeomorphic to an open disk. We compactify this orbit space with an ideal circle boundary. If there are no perfect fits between stable and unstable leaves and the flow is not topologically conjugate to …
The paper extends circle pattern flows to hyperbolic and Euclidean geometry.
In this article we obtain a simple topological and dynamical systems condition which is necessary and sufficient for an arbitrary pseudo-Anosov flow in a closed, hyperbolic three manifold to be quasigeodesic. Quasigeodesic means that orbits are efficient in measuring length up to a bounded multiplicative distortion whe…
Study shows universal circle isomorphic to flow space ideal boundary.
Multiplier ideal sheaves are constructed as obstructions to the convergence of the Kähler-Ricci flow on Fano manifolds, following earlier constructions of Kohn, Siu, and Nadel, and using the recent estimates of Kolodziej and Perelman
The paper studies ideal flows of closed curves, classifying critical points and proving flow behavior.
Proves unique hyperbolic metric for 3-manifolds with ideal triangulation.
Paper resolves spherical curvature flow problem.
The purpose of this paper is to calculate the support of the multiplier ideal sheaves derived from the Kähler-Ricci flow on certain toric Fano manifolds with large symmetry. The early idea of this paper has already been in Appendix of \cite{futaki-sano0711}.
S. K. Donaldson asked whether the lower bound of the Calabi functional is achieved by a sequence the normalized Donaldson-Futaki invariants. We answer the question for the Ricci curvature formalism, in place of the scalar curvature. The principle is that the stability indicator is optimized by the multiplier ideal shea…
On certain del Pezzo surfaces with large automorphism groups, it is shown that the solution to the Kähler-Ricci flow with a certain initial value converges in -norm exponentially fast to a Kähler-Einstein metric. The proof is based on the method of multiplier ideal sheaves.
Paper proves Luo's conjecture for 3D triangulated manifolds.
In this note we construct Nadel multiplier ideal sheaves using the Ricci flow on Fano manifolds. This extends a result of Phong, Sesum and Sturm. These sheaves, like their counterparts constructed by Nadel for the continuity method, can be used to obtain an existence criterion for Kahler-Einstein metrics.
Classifies pseudo-Anosov flows on 3-manifolds up to orbit equivalence.
The paper studies the combinatorial p-th Calabi flow for finite and infinite circle patterns.
The paper proves a combinatorial Ricci flow converges to hyperbolic structures on certain 3-manifolds.
The paper finds hyperbolic metrics on surfaces with boundary using combinatorial curvature flows.
This paper contains a generalization of the convex ideal case of the Thurston-Andreev theorem when the genus is greater than 1. The heart of the paper concerns taking formal angle data on a surface and ``conformally flowing'' this formal angle data to uniquely associated uniform angle data. This flow turns out to be th…
New criteria for ideal circle patterns on surfaces.
The article confirms Thurston's conjecture for a specific class of 3-manifolds using combinatorial Ricci flow.
Paper extends port-Hamiltonian model to include internal energy for compressible and incompressible flow.
Paper develops a new fluid flow model with energy exchange through boundaries.
We study the blowup behavior at infinity of the normalized Kahler-Ricci flow on a Fano manifold which does not admit Kahler-Einstein metrics. We prove an estimate for the Kahler potential away from a multiplier ideal subscheme, which implies that the volume forms along the flow converge to zero locally uniformly away f…
By proving precisely which singularity index lists arise from the pair of invariant foliations for a pseudo-Anosov surface homeomorphism, Masur and Smillie determined a Teichmüller flow invariant stratification of the space of quadratic differentials. In this final paper of a three-paper series, we give a first step to…
We consider the evolution of a compact segment of an analytic curve on the unit tangent bundle of a finite volume hyperbolic -manifold under the geodesic flow. Suppose that the curve is not contained in a stable leaf of the flow. It is shown that under the geodesic flow, the normalized parameter measure on the curve…
The study identifies conjugate and cut points in ideal fluid motion configurations.
Paper finds sparse representation of functions using inverse scale space flow.
A large class of variational equations for geometric objects is studied. The results imply conformal monotonicity and Liouville theorems for steady, polytropic, ideal flow, and the regularity of weak solutions to generalized Yang-Mills and Born-Infeld systems.
Investigates fluid flow perturbations using geometric theory.
The paper applies combinatorial Ricci flows to prove hyperbolic structures on 3-manifolds.
In this paper we use a gradient flow to deform closed planar curves to curves with least variation of geodesic curvature in the sense. Given a smooth initial curve we show that the solution to the flow exists for all time and, provided the length of the evolving curve remains bounded, smoothly converges to a mult…
The paper explores the geometric properties of fluid flows and their symmetries.
The paper introduces combinatorial Calabi flows to find hyperbolic metrics on surfaces with boundary.
Paper introduces VDE, a variance-reduced determinant estimator.
It is known that principal orbits of Hermann actions on a symmetric space of non-compact type are curvature-adapted isoparametric submanifolds having no focal point of non-Euclidean type on the ideal boundary of the ambient symmetric space. In this paper, we investigate the mean curvature flows for such a curvature-ada…
Harmonic maps from complex plane to hyperbolic space constructed using heat flow.
We study the supremum of the volume of hyperbolic polyhedra with some fixed combinatorics and with vertices of any kind (real, ideal or hyperideal). We find that the supremum is always equal to the volume of the rectification of the 1-skeleton. The theorem is proved by applying a sort of volume-increasing flow to any h…
We study the Riemannian geometry of 3D axisymmetric ideal fluids. We prove that the exponential map on the group of volume-preserving diffeomorphisms of a -manifold is Fredholm along axisymmetric flows with sufficiently small swirl. Along the way, we define the notions of axisymmetric and swirl-free diffeomorp…
This paper uses combinatorial Ricci flow to tackle Thurston's triangulation conjecture.
In this paper, we study the Ricci flow of solvmanifolds whose Lie algebra has an abelian ideal of codimension one, by using the bracket flow. We prove that solutions to the Ricci flow are immortal, the omega-limit of bracket flow solutions is a single point, and that for any sequence of times there exists a subsequence…
The paper studies a flow on complex Lie groups, showing convergence to solitons.
Review of diffusion models for SBI in non-ideal data scenarios.