Related papers: Evolve nondegenerate two forms

We consider the 1-harmonic flow of maps from a bounded domain into a submanifold of a Euclidean space, i.e. the gradient flow of the total variation functional restricted to maps taking values in the manifold. We restrict ourselves to…

Ancient solutions of the Ricci flow arise naturally as models for singularity formation. There has been significant progress towards the classification of such solutions under natural geometric assumptions. Nonnegatively curved solutions in…

We show uniqueness of Ricci flows starting at a surface of uniformly negative curvature, with the assumption that the flows become complete instantaneously. Together with the more general existence result proved in [10], this settles the…

In this note we study conformal Ricci flow introduced by Arthur Fischer. We use DeTurck's trick to rewrite conformal Ricci flow as a strong parabolic-elliptic partial differential equations. Then we prove short time existences for conformal…

There is a common description of different intrinsic geometric flows in two dimensions using Toda field equations associated to continual Lie algebras that incorporate the deformation variable t into their system. The Ricci flow admits zero…

We study singularity formation of complete Ricci flow solutions, motivated by two applications: (a) improving the understanding of the behavior of the essential blowup sequences of Enders-Muller-Topping on noncompact manifolds, and (b)…

We study the generalized K\"ahler-Ricci flow on complex surfaces with nondegenerate Poisson structure, proving long time existence and convergence of the flow to a weak hyperK\"ahler structure.

We establish a short-time existence theory for complete Ricci flows under scaling-invariant curvature bounds, starting from rotationally symmetric metrics on $\mathbb{R}^{n+1}$ that are noncollapsed at infinity, without assuming bounded…

We prove uniqueness of instantaneously complete Ricci flows on surfaces. We do not require any bounds of any form on the curvature or its growth at infinity, nor on the metric or its growth (other than that implied by instantaneous…

Partially invariant solution to (2+1)D shallow water equation is constructed and investigated. The solution describes an extension of a stripe, bounded by linear source and drain of fluid. Realizations of smooth flow and of hydraulic jump…

While normalizing flows have led to significant advances in modeling high-dimensional continuous distributions, their applicability to discrete distributions remains unknown. In this paper, we show that flows can in fact be extended to…

We consider four extended Ricci flow systems---that is, Ricci flow coupled with other geometric flows---and prove dynamical stability of certain classes of stationary solutions of these flows. The systems include Ricci flow coupled with…

Let $(M^3,g_0)$ be a complete noncompact Riemannian 3-manifold with nonnegative Ricci curvature and with injectivity radius bounded away from zero. Suppose that the scalar curvature $R(x)\to 0$ as $x\to \infty$. Then the Ricci flow with…

The 2D Ricci flow equation in the conformal gauge is studied using the linearization approach. Using a non-linear substitution of logarithmic type, the emergent quadratic equation is split in various ways. New special solutions involving…

For an ancient Ricci flow asymptotic to a compact integrable shrinker, or a Ricci flow developing a finite-time singularity modelled on the shrinker, we establish the long-time existence of a harmonic map heat flow between the Ricci flow…

In this paper we derive a two-component system of nonlinear equations which model two-dimensional shallow water waves with constant vorticity. Then we prove well-posedness of this equation using a geometrical framework which allows us to…

We prove that for any complete three-manifold with a lower Ricci curvature bound and a lower bound on the volume of balls of radius one, a solution to the Ricci flow exists for short time. Actually our proof also yields a (non-canonical)…

We extend the notion of what it means for a complete Ricci flow to have a given initial metric, and consider the resulting well-posedness issues that arise in the 2D case. On one hand we construct examples of nonuniqueness by showing that…

In this work, we first establish short time existence and Shi's type estimate of second Ricci flow on complete noncompact Hermitian manifolds. As an application, we use the second Ricci flow to discuss the existence of Kaehler-Einstein…

We are interested in an anisotropic singular diffusion equation in the plane and in its regularization. We establish existence, uniqueness and basic regularity of solutions to both equations. We construct explicit solutions showing the…