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We generalize most of the known Ricci flow invariant non-negative curvature conditions to less restrictive negative bounds that remain sufficiently controlled for a short time. As an illustration of the contents of the paper, we prove that…
We study Ricci flows of some classes of physically valuable solutions in Einstein and string gravity. The anholonomic frame method is applied for generic off-diagonal metric ansatz when the field/ evolution equations are transformed into…
The identification of platforms with independently tunable nonlinearity and non-Hermiticity promises a quantitative route to far-from-equilibrium universality across many-body systems. Here we show that a conventional ferromagnetic…
We construct a class of stationary, axisymmetric, horizonless spacetimes whose curvature is generated entirely by smooth, localised differential rotation $\Omega(r)$, while the spatial geometry remains exactly flat. Despite vanishing ADM…
The famous Uniformization Theorem states that on closed Riemannian surfaces there always exists a metric of constant curvature for the Levi-Cevita connection. In this article we prove that an analogue of the uniformization theorem also…
In this paper we propose a class of local definitions of weak lower scalar curvature bounds that is well defined for $C^0$ metrics. We show the following: that our definitions are stable under greater-than-second-order perturbation of the…
We show how solutions to the Ricci flow on Lorentzian manifolds, along with its generalizations, can be linked to Einstein's field equations. The approach involves deformations of the matter sector that are generated by quadratic…
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to…
We review the main aspects of Ricci flows as they arise in physics and mathematics. In field theory they describe the renormalization group equations of the target space metric of two dimensional sigma models to lowest order in the…
At a critical ``chiral'' coupling, topologically massive gravity with a negative cosmological constant exhibits several unusual features, including the emergence of a new logarithmic branch of solutions and a linearization instability for…
We present a family of electron-based coupled-wire models of bosonic orbifold topological phases, referred to as twist liquids, in two spatial dimensions. All local fermion degrees of freedom are gapped and removed from the topological…
We introduce two new functionals on Sasaki manifolds, inspired by the work of Perelman, which are monotonic along the Sasaki-Ricci flow. We relate their gradient flow, via diffeomorphisms preserving the foliated structure of the manifold,…
We study a time-reversal invariant vortex, namely a spin vortex, in helical superconductors by focusing on its emergent gravitational structure. The topology of the time-reversal invariant vortex is classified by a $\mathbb{Z}_2$ invariant:…
We provide a comparatively simple proof of the dynamical stability of Ricci flow near a linearly stable Ricci-flat ALE metric with integrable deformations. Our proof relies on the equivalence between integrability and an…
We design strategies in nonlinear geometric analysis to temper the effects of adversarial learning for sufficiently smooth data of numerical method-type dynamics in encoder-decoder methods, variational and deterministic, through the use of…
We analyse the stability issue of the vector and axial modes of the torsion and nonmetricity tensors around general backgrounds in the framework of cubic Metric-Affine Gravity. We show that the presence of cubic order invariants defined…
We find exact solutions describing Ricci flows of four dimensional pp-waves nonlinearly deformed by two/three dimensional solitons. Such solutions are parametrized by five dimensional metrics with generic off-diagonal terms and connections…
We propose an alternative route to stabilize magnetic skyrmion textures which does not require Dzyaloshinkii-Moriya interaction, magnetic anisotropy, or an external Zeeman field. Instead, it solely relies on the emergence of flux in the…
We present laboratory experiments on turbulence in a linearly stratified fluid driven by an ensemble of internal gravity waves which approaches statistical homogeneity and axi-symmetry. In a way similar to several recent experimental works,…
We prove the existence of a one-parameter family of pairwise non-isometric, complete, positively curved, steady generalized Ricci solitons of gradient type on $\mathbb{R}^3$ that are invariant under the natural cohomogeneity one action of…