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.
Paper proves uniqueness of weak solutions for Plateau flow.
Study weak super Ricci flow through neckpinch in metric measure spaces.
Smooth flows with surgery approximate weak mean curvature flows with spherical and neck-pinch singularities.
Study proves existence of weak mean curvature flow with contact angle.
New formulations for Ricci flows without smoothness.
We provide a direct proof of time-slice weak compactness along the Kähler Ricci flow on Fano manifolds.
New boundary condition for weak inverse mean curvature flow in bounded domains.
Study shows how weak inverse anisotropic mean curvature flow behaves at infinity.
We prove the existence and uniqueness of the weak Kahler-Ricci flow on projective varieties with log terminal singularities. It is also shown that the weak Kahler-Ricci flow can be uniquely continued through divisorial contractions and flips if they exist. We then propose an analytic version of the Minimal Model Progra…
Novel weak solutions for volume-preserving mean curvature flow established.
New varifold solutions for mean curvature flow converge and are unique.
Study finds weak solutions for complex map flows with optimal lifespan.
Minimal existence time for Willmore flow established for smooth and weak Lipschitz initial data.
Develops weak formulation for spacelike flows in pseudo-Euclidean space.
Paper reconciles different Ricci flow approaches and proves weak solutions.
In an earlier work joint with X. X. Chen and G. Tian, we introduced the weak Kähler-Ricci flow for various geometric motivations. In the current work, we take further consideration on setting up the weak flow. Namely, the initial class is allowed to be no longer Kähler.
In this paper, we prove the long-time existence and uniqueness of the conical Kähler-Ricci flow with weak initial data which admits density for some on Fano manifold. Furthermore, we study the convergence behavior of this kind of flow.
Alternative proof of weak solutions to mean curvature flow using minimizing movements.
Surveying Ricci flow for weak lower scalar curvature bounds.
Proves existence of proper solutions for inverse mean curvature flow.
Proves higher regularity for anisotropic inverse mean curvature flow.
Weak base-point freeness leads to Kähler-Ricci flow diameter bounds.
Lipschitz regularity proved for harmonic map heat flows into CAT(0) spaces.
We study the mean curvature flow with given non-smooth transport term and forcing term, in suitable Sobolev spaces. We prove the global existence of the weak solutions for the mean curvature flow with the terms, by using the modified Allen-Cahn equation that holds useful properties such as the monotonicity formula.
A new parametric method studies Willmore flows and energy quantization.
In this paper, we continue to study the Calabi flow on complex tori. We develop a new method to obtain an explicit bound of the curvature of the Calabi flow. As an application, we show that when , the Calabi flow starting from a weak Kähler metric will become smooth immediately. It implies that in our settings, th…
In this note, we prove the existence of weak solutions of the Chern-Ricci flow through blow downs of exceptional curves, as well as backwards smooth convergence away from the exceptional curves on compact complex surfaces. The smoothing property for the Chern-Ricci flow is also obtained on compact Hermitian manifolds o…
By making use of the nice behavior of Hawking masses of slices of a weak solution of inverse mean curvature flow in three dimensional asymptotically hyperbolic manifolds, we are able to show that each slice of the flow is star-shaped after a long time, and then we get the regularity of the weak solution of inverse mean…
New non-canonical flows found via parabolic Allen-Cahn equations.
Self-test loss functions improve data-driven modeling of weak-form operators and gradient flows.
The paper studies limits of flows on Kähler surfaces, proving convergence to solutions of equations.
Study constructs solutions for evolving hypersurfaces using inverse spacetime mean curvature.
In this paper, we prove that on a Fano manifold which admits a Kähler-Ricci soliton $(\om,X)$, if the initial Kähler metric $\om_{\vphi_0}$ is close to $\om$ in some weak sense, then the weak Kähler-Ricci flow exists globally and converges in Cheeger-Gromov sense. Moreover, if $\vphi_0$ is also -invariant, the…
Paper shows how to transform certain flows into R-covered ones.
We study the phase field method for the volume preserving mean curvature flow. Given an initial hypersurface we proved the existence of the weak solution for the volume preserving mean curvature flow via the reaction diffusion equation with a nonlocal term. We also show the monotonicity formula and the density up…
Study on test risk dynamics in learning theory with stochastic gradient flow.
We consider the problem of evolving hypersurfaces by mean curvature flow in the presence of obstacles, that is domains which the flow is not allowed to enter. In this paper, we treat the case of complete graphs and explain how the approach of M. Saez and the second author yields a global weak solution to the original p…
Studying the (long-term) behavior of the Kähler-Ricci flow on mildly singular varieties, one is naturally lead to study weak solutions of degenerate parabolic complex Monge-Ampére equations. The purpose of this article, the second of a series on this subject, is to develop a viscosity theory for degenerate complex Mong…
Long time existence and convergence to a circle is proved for radial graph solutions to a mean curvature type curve flow in warped product surfaces (under a weak assumption on the warp potential of the surface). This curvature flow preserves the area enclosed by the evolving curve, and this fact is used to prove a gene…
This is the first of a series of papers, where we introduce a new class of estimates for the Ricci flow, and use them both to characterize solutions of the Ricci flow and to provide a notion of weak solutions to the Ricci flow in the nonsmooth setting. In this first paper, we prove various new estimates for the Ricci f…
We prove the existence of a unique global weak solution to the full bosonic string heat flow from closed Riemannian surfaces to an arbitrary target under smallness conditions on the two-form and the scalar potential. The solution is smooth with the exception of finitely many singular points. Finally, we discuss the con…
Studying the behavior of the Kähler-Ricci flow on mildly singular varieties, one is naturally lead to study weak solutions of degenerate parabolic complex Monge-Ampère equations. In this article, the third of a series on this subject, we study the long term behavior of the normalized Kähler-Ricci flow on mildly singula…
We consider a continuous curve of self-adjoint Fredholm extensions of a curve of closed symmetric operators with fixed minimal domain and fixed {\it intermediate} domain . Our main example is a family of symmetric generalized operators of Dirac type on a compact manifold with boundary with varying well-posed…
We give a proof that Brakke's mean curvature flow under the unit density assumption is smooth almost everywhere in space-time. More generally, if the velocity is equal in a weak sense to its mean curvature plus some given α-Hölder continuous vector field, then we show C^{2,α} regularity almost everywhere.
We give a new proof of Brakke's partial regularity theorem up to C^{1,ς} for weak varifold solutions of mean curvature flow by utilizing parabolic monotonicity formula, parabolic Lipschitz approximation and blow-up technique. The new proof extends to a general flow whose velocity is the sum of the mean curvature and an…
New heat flow for harmonic maps avoids singularities but not bubbles.
We prove the smoothness of weak solutions to an elliptic complex Monge-Ampere equation, using the smoothing property of the corresponding parabolic flow.
In this note, we define and study Kähler-Ricci flow with initial data not being smooth with some natural applications.