Related papers: A note on the quantum-mechanical Ricci flow
The Ricci iteration is a discrete analogue of the Ricci flow. According to Perelman, the Ricci flow converges to a Kahler-Einstein metric whenever one exists, and it has been conjectured that the Ricci iteration should behave similarly.…
The Ricci flow is a heat equation for metrics, which has recently been used to study the topology of closed three manifolds. In this paper we apply Ricci flow techniques to general relativity. We view a three dimensional asymptotically flat…
We investigate the effects of given pressure gradients on hydrodynamic flow equations. We obtain results in terms of implicit solutions and also in the framework of an extra-dimensional formalism involving the diffusion/Schrodinger…
We find the regime of our recently constructed topological nonrelativistic quantum gravity, in which Perelman's Ricci flow equations on Riemannian manifolds appear precisely as the localization equations in the path integral. In this…
There are described equations for a pair comprising a Riemannian metric and a Killing field on a surface that contain as special cases the Einstein Weyl equations (in the sense of D. Calderbank) and a real version of a special case of the…
In this paper we present several curvature estimates and convergence results for solutions of the Ricci flow. The curvature estimates depend on smallness of certain local space-time integrals of the norm of the Riemann curvature tensor,…
The Schr\"odinger-type formalism of the Klein-Gordon quantum mechanics is adapted for the case of the $SL(2,\R)$ spacetime. The free particle case is solved, the results of a recent work are reproduced while all the other, topologically…
We review different notions of synthetic Ricci flow that apply to time-dependent families of metric measure spaces and which are based on properties of the heat flow, ideas from optimal transport, and the asymptotic behaviour of volumes.…
We study the behavior of a three-dimensional dynamical system with respect to some set $S$ given in 3-dimensional euclidian space. Geometrically such a system arises from the normalized Ricci flow on some class of generalized Wallach spaces…
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…
On a compact Riemannian manifold, we study the various dynamical properties of the Schr\"odinger flow $(e^{it\Delta/2})$, through the notion of semiclassical measures and the quantum-classical correspondence between the Schr\"odinger…
We formulate a statistical analogy of regular Lagrange mechanics and Finsler geometry derived from Grisha Perelman's functionals generalized for nonholonomic Ricci flows. There are elaborated explicit constructions when nonholonomically…
This paper attempts to construct monotonic entropy functionals for four-dimensional Lorentzian spacetime under physical boundary conditions, as an extension of Perelman's monotonic entropy functionals constructed for three-dimensional…
In this short paper, we propose a new quantum effect that naturally emerges from describing the quantum particle as a classical fluid. Following the hydrodynamical formulation of quantum mechanics for a particle in a finite convex region,…
In this survey we provide an overview of our recent results concerning Ricci de Turck flow on spaces with isolated conical singularities. The crucial characteristic of the flow is that it preserves the conical singularity. Under certain…
We give some heuristic results for FRW situations with Ricci flow.
This is the second paper in a series of works devoted to nonholonomic Ricci flows. By imposing non-integrable (nonholonomic) constraints on the Ricci flows of Riemannian metrics we can model mutual transforms of generalized Finsler-Lagrange…
We introduce a flow of Riemannian metrics over compact manifolds with formal limit at infinite time a shrinking Ricci soliton. We call this flow the Soliton-Ricci flow. It correspond to a Perelman's modified backward Ricci type flow with…
We derive estimates relating the values of a solution at any two points to the distance between the points, for quasilinear parabolic equations on compact Riemannian manifolds under the Ricci flow.
The Schr\"odinger equation is shown to be equivalent to a constrained Liouville equation under the assumption that phase space is extended to Grassmann algebra valued variables. For onedimensional systems, the underlying Hamiltonian…