Related papers: Soliton metrics for two-loop renormalization group…
This paper studies the normalized Ricci flow on surfaces with conical singularities. It's proved that the normalized Ricci flow has a solution for a short time for initial metrics with conical singularities. Moreover, the solution makes…
We classify spin ALE ancient Ricci flows and spin ALE expanding solitons with suitable groups at infinity. In particular, the only spin ancient Ricci flows with groups at infinity in $SU(2)$ and mild decay at infinity are hyperk\"ahler ALE…
A recently proposed renormalization group technique, based on the hierarchical structures present in theories with fluctuating geometry, is implemented in the model of branched polymers. The renormalization group equations can be solved…
We study families of solitons in a two-dimensional (2D) model of the light transmission through a photorefractive medium equipped with a (quasi-)one-dimensional photonic lattice. The soliton families are bounded from below by finite minimum…
We consider a closed manifold M with a Riemannian metric g(t) evolving in direction -2S(t) where S(t) is a symmetric two-tensor on (M,g(t)). We prove that if S satisfies a certain tensor inequality, then one can construct a forwards and a…
This paper studies cohomogeneity one Ricci solitons. If the isotropy representation of the principal orbit $G/K$ consists of two inequivalent $Ad_K$-invariant irreducible summands, the existence of parameter families of non-homothetic…
We demonstrate that any four-dimensional shrinking Ricci soliton $(\mathcal B \times {\mathbb S^2}, g)$, where $\mathcal B$ is any two-dimensional complete noncompact surface and $g$ is a warped product metric over the base $\mathcal B$,…
We study stability of non-compact gradient Kaehler-Ricci flow solitons with positive holomorphic bisectional curvature. Our main result is that any compactly supported perturbation and appropriately decaying perturbations of the Kaehler…
The quantum field theory of two-dimensional sigma models with bulk and boundary couplings provides a natural framework to realize and unite different species of geometric flows that are of current interest in mathematics. In particular, the…
Quasi-Einstein manifolds are well-studied generalizations of Einstein manifolds. This includes gradient Ricci solitons and has a natural correspondence with the warped product Einstein manifolds. A quasi-Einstein metric is said to be rigid…
We show how to associate with each graph with a certain property (positivity) a family of simply connected solvable Lie groups endowed with left-invariant Riemannian metrics that are Ricci solitons (called solsolitons). We classify them up…
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of…
If g(t) is a three-dimensional Ricci flow solution, with sectional curvatures that decay like the inverse of t and diameter that increases at most like the square root of t, then the pullback Ricci flow solution on the universal cover…
This paper explores the evolution and monotonicity of geometric constants within the framework of extended Ricci flows, incorporating variable coupling parameters. Building on Hamiltons foundational Ricci flow and subsequent extensions by…
We study the two-dimensional renormalization-group flow induced by perturbations that reduce the global symmetry of the O(3) sigma-model to the discrete symmetries of Platonic solids. We estimate the value of the correlation length at which…
For any $n\geq 4$, we construct an $(n-2)$-parameter family of steady gradient Ricci solitons with non-negative curvature operator and prescribed by the eigenvalues of Ricci tensor at a critical point of the soliton potential. Among them…
Recently, it was shown that Einstein solvmanifolds have maximal symmetry in the sense that their isometry groups contain the isometry groups of any other left-invariant metric on the given Lie group. Such a solvable Lie group is necessarily…
In this paper we study the gradient Ricci shrinking soliton equation on rotationally symmetric manifolds of dimension three and higher and prove that the only complete examples of such metrics on $S^n$, $\R{n}$ and $\R{}\times S^{n-1}$ are,…
Interpreting renormalization group flows as solitons interpolating between different fixed points, we ask various questions that are normally asked in soliton physics but not in renormalization theory. Can one count RG flows? Are there…
We discuss the renormalization group flow, duality, and supersymmetry breaking in N = 1 supersymmetric SU(N)xSU(M) gauge theories.