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 finite time singularities in Ricci flow with bounded scalar curvature.
Ricci flow singularities on compact Kähler surfaces are of Type I.
The paper analyzes finite-time singularities in Spin(7)-structure flows using Shi-type estimates.
In this note we study finite-time singularities in the Chern-Ricci flow. We show that finite-time singularities are characterized by the blow-up of the scalar curvature of the Chern connection.
In this short paper, we show that Kähler-Ricci flows over closed manifolds would have scalar curvature blown-up for finite time singularity. Certain control of the blowing-up is achieved with some mild assumption.
Study K-R flow on Hirzebruch surfaces, showing tangent flows are K-R flows with orbifold singularities.
The paper examines Ricci flows with closed and smooth tangent flows, proving uniqueness and characterizing ancient flows.
Given any embedded Lagrangian on a four dimensional compact Calabi-Yau, we find another Lagrangian in the same Hamiltonian isotopy class which develops a finite time singularity under mean curvature flow. This contradicts a weaker version of the Thomas-Yau conjecture regarding long time existence and convergence of Lag…
Enhances understanding of Kähler-Ricci flow singularities.
The Kähler-Ricci flow's singularities are analyzed with bounds and convergence results.
Study Kähler-Ricci flow on manifolds with singularities.
Constructs finite-time singularities in Lagrangian mean curvature flow with precise dynamics.
In this paper, we extend Lotay-Wei's Shi-type estimate from Laplacian flow to more general flows of G structures including the modified Laplacian co-flow. Then we prove a version of -non-collapsing theorem. We will use both of them to study finite time singularities of general flows of G structures.
Harmonic map flow's singularity properties proven with Lojasiewicz inequalities.
New study confirms some mean curvature flow solutions have bounded mean curvature.
We show that if on a compact Kahler threefold there is a solution of the Kahler-Ricci flow which encounters a finite time collapsing singularity, then the manifold admits a Fano fibration. Furthermore, if there is finite time extinction then the manifold is Fano and the initial class is a positive multiple of the first…
Researchers found a new type of singularity in surface evolution equations.
Curve shortening flow converges to a point with entropy bound.
New heat flow for harmonic maps avoids singularities but not bubbles.
Strict type-II blowup in harmonic map flow is proven to have Hölder continuous body map.
Paper studies smoothness of bi-conformal heat flow on 4-manifolds.
Study verifies Joyce's conjectures for circle-invariant Lagrangian surfaces.
Estimates for VPMCF show ancient MCF solutions and finite-time behavior.
We study "warped Berger" solutions $\big(\mc S^1\times\mc S^3,G(t)\big)$ of Ricci flow: generalized warped products with the metric induced on each fiber a left-invariant Berger metric. We prove that this structure is preserved by the flow, that these solutions develop finite-time neckpinch …
Paper studies heat flow for maps on manifolds, avoiding singularities.
Paper shows perturbed Taub-Bolt metric becomes singularity under Ricci flow.
Study on singularities of Chern-Ricci flow on complex manifolds.
We study finite-time collapsing limits of the continuity method. When the continuity method starting from a rational initial Kähler metric on a projective manifold encounters a finite-time volume collapsing, this projective manifold admits a Fano fibration over a lower dimensional base. In this case, we prove the conti…
Constructing eigenfunctions for finite-time singularities in Lagrangian mean curvature flow
Study Ricci flow on CP1-bundles over Kähler-Einstein manifolds.
The article explores Helfrich flow with spontaneous curvature, finding singularities and convergence behaviors.
Finite-time extinction and smoothing effects in fractional fast diffusion on manifolds.
We study the convergence of complete non-compact conformally flat solutions to the Yamabe flow to Yamabe steady solitons. We also prove the existence of Type II singularities which develop at either a finite time or as .
We prove that the scalar curvature of a homogeneous Ricci flow solution blows up at a forward or backward finite-time singularity.
We establish fundamental results for a parabolic flow of Riemannian metrics introduced by Bahuaud-Helliwell in arXiv:1010:4287v1 which is based on the Fefferman-Graham ambient obstruction tensor. First, we obtain local smoothing estimates for the curvature tensor and use them to prove pointwise smoothing estimate…
Ricci flow modelled on specific singularities on closed manifolds.
Compact mean curvature flow solutions with bounded curvature in high dimensions are constructed.
Study classifies bubbles of Type I singularities in Kähler-Ricci flow on compact surfaces.
We show that timelike maximal cylinders in $\RR^{1 + 2}$ always develop singularities in finite time and that, infinitesimally at a generic singularity, their time slices are evolved by a rigid motion or a self-similar motion. We also prove a mild generalization in non-flat backgrounds.
In this note we establish that finite-time singularities of the mean curvature flow of compact Riemannian submanifolds are characterised by the blow up of the mean curvature.
We analyse finite-time singularities of the Teichmüller harmonic map flow -- a natural gradient flow of the harmonic map energy -- and find a canonical way of flowing beyond them in order to construct global solutions in full generality. Moreover, we prove a no-loss-of-topology result at finite time, which completes th…
A submanifold in space forms is isoparametric if the normal bundle is flat and principal curvatures along any parallel normal fields are constant. We study the mean curvature flow with initial data an isoparametric submanifold in Euclidean space and sphere. We show that the mean curvature flow preserves the isoparametr…
In this paper, we study the singularities of two extended Ricci flow systems --- connection Ricci flow and Ricci harmonic flow using newly-defined curvature quantities. Specifically, we give the definition of three types of singularities and their corresponding singularity models, and then prove the convergence. In add…
Paper shows no finite time singularities for smooth conformal heat flow of harmonic maps.
We investigate Riemannian (non-Kahler) Ricci flow solutions that develop finite-time Type-I singularities and present evidence in favor of a conjecture that parabolic rescalings at the singularities converge to singularity models that are shrinking Kahler-Ricci solitons. Specifically, the singularity model for these so…
Given a singular Riemannian foliation on a compact Riemannian manifold, we study the mean curvature flow equation with a regular leaf as initial datum. We prove that if the leaves are compact and the mean curvature vector field is basic, then any finite time singularity is a singular leaf, and the singularity is of typ…
In this note we investigate the behaviour at finite-time singularities of the mean curvature flow of compact Riemannian submanifolds M^m_t\hookrightarrow (N^{m+n}, h). We show that they are characterized by the blow-up of a trace A = H \cdot II of the square of the second fundamental form.
We study noncompact surfaces evolving by mean curvature flow. Without any symmetry assumptions, we prove that any solution that is -close at some time to a standard neck will develop a neckpinch singularity in finite time, will become asymptotically rotationally symmetric in a space-time neighborhood of its singul…