Related papers: Ricci flows, wormholes and critical phenomena
We propose, as a novelty in the literature, the modelling of wormholes within the particular case of the $f(R,T)$ gravity, namely $f(R,T)=R+\alpha R^{2}+\lambda T$, with $R$ and $T$ being the Ricci scalar and trace of the energy-momentum…
In a singular Type I Ricci flow, we consider a stratification of the set where there is curvature blow-up, according to the number of the Euclidean factors split by the tangent flows. We then show that the strata are characterized roughly…
Space-time wormholes were introduced in Wheeler's idea of space-time foam. Traversible wormholes as defined by Morris & Thorne became popular as potential short cuts across the universe and even time machines. More recently, the author…
We study relation of the Ricci Flow on 3-dimensional Lie groups and 4-dimensional Ricci-flat manifolds. In particular, we construct Ricci-flat cohomogeneity one metrics with respect to 3-dimensional Lie groups.
Beginning with a brief review of the regular space-time with asymptotically Minkowski core, we can consider two copies of the space-time connected through a short-throat wormhole whose radius of mouth is equal to or larger than an extremal…
Deep neural networks learn feature representations via complex geometric transformations of the input data manifold. Despite the models' empirical success across domains, our understanding of neural feature representations is still…
We develop a stochastic target representation for Ricci flow and normalized Ricci flow on smooth, compact surfaces, analogous to Soner and Touzi's representation of mean curvature flow. We prove a verification/uniqueness theorem, and then…
We consider the Kaehler-Ricci flow on complete finite-volume metrics that live on the complement of a divisor in a compact Kaehler manifold X. Assuming certain spatial asymptotics on the initial metric, we compute the singularity time in…
In this paper, we consider functionals related to mean curvature flow in an ambient space which evolves by an extended Ricci flow from the perspective introduced by Lott when studying a mean curvature flow in a Ricci flow background. One of…
We give a surface for which the Ricci Flow applied to the metric will increase the topological entropy of the geodesic flow. Specifically, we first adapt the Melnikov method to apply to a Ricci Flow perturbation and then we construct a…
Spacetime wormholes in isotropic spacetimes are represented traditionally by embedding diagrams which were symmetric paraboloids. This mirror symmetry, however, can be broken by considering different sources on different sides of the…
We give biLipschitz models for the Ricci flow on some 4-manifolds (minimal surfaces of general type), exhibiting a combination of expanding and static behavior.
Spatio-temporally complex flows are found at the onset of unsteadiness in (axisymmetric) rotor-stator turbulence in the shape of concentric rolls. The emergence of these rolls is rationalised using a homotopy approach, where the original…
We show stability of pairs of Ricci flat metrics and parallel spinor fields with respect to the spinor flow, i.e. we show that the spinor flow with initial conditions near such pairs converges to a critical point with exponential speed.…
In this paper, we introduce a new notion of curvature on the edges of a graph that is defined in terms of effective resistances. We call this the Ricci--Foster curvature. We study the Ricci flow resulting from this curvature. We prove the…
We study the four dimensional Ricci flow with the help of local invariants. If $(M^4, g(t))$ is a solution to the Ricci flow and $x \in M^4$, we can associate to the point $x$ a one-parameter family of curves, which lie in the product of…
We consider the problem of deforming a one-parameter family of hypersurfaces immersed into closed Riemannian manifolds with positive curvature operator. The hypersurface in this family satisfies mean curvature flow while the ambient metric…
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…
We consider the asymptotic behavior of the normalized Ricci flow on generalized Wallach spaces that could be considered as special planar dynamical systems. All non symmetric generalized Wallach spaces can be naturally parametrized by three…
We consider the dynamical Morris-Thorne metric with radiating heat flow. By matching the interior Morris-Thorne metric with an exterior Vaidya metric we trace out the collapse solutions for the corresponding spherically symmetric…