Related papers: The Anomaly flow on nilmanifolds

We introduce a new family of thermostat flows on the unit tangent bundle of an oriented Riemannian $2$-manifold. Suitably reparametrised, these flows include the geodesic flow of metrics of negative Gauss curvature and the geodesic flow…

Two-dimensional free-surface flow over localised topography is examined with the emphasis on the stability of hydraulic-fall solutions. A Gaussian topography profile is assumed with a positive or negative amplitude modelling a bump or a…

In this paper, we study critical points and gradient flows of the $G_2$--Hilbert functional on a manifolds with free $\mathbb S^1$--actions. We analyze $\mathbb S^1$--invariant $G_2$--structures under the constant fiber-length non-K\"ahler…

We study the behaviour of the normalized K\"ahler-Ricci flow on complete K\"ahler manifolds of negative holomorphic sectional curvature. We show that the flow exists for all time and converges to a K\"ahler-Einstein metric of negative…

We define a new geometric flow, which we shall call the $K$-flow, on 3-dimensional Riemannian manifolds; and study the behavior of Thurston's model geometries under this flow both analytically and numerically. As an example, we show that an…

Geometric flows have proved to be a powerful geometric analysis tool, perhaps most notably in the study of 3-manifold topology, the differentiable sphere theorem, Hermitian-Yang-Mills connections and canonical Kaehler metrics. In the…

A geometric flow on $(2,2)$-forms is introduced which preserves the balanced condition of metrics, and whose stationary points satisfy the anomaly equation in Strominger systems. The existence of solutions for a short time is established,…

In this paper, we study the $t$-Gauduchon Ricci-flat condition under the Chern-Ricci flow. In this setting, we provide examples of Chern-Ricci flow on compact non-K\"ahler Calabi-Yau manifolds which do not preserve the $t$-Gauduchon…

We study 't Hooft anomalies and the related anomaly inflow for subsystem global symmetries. These symmetries and anomalies arise in a number of exotic systems, including models with fracton order such as the X-cube model. As is the case for…

We study the asymptotic behavior of the pluriclosed flow in the case of left-invariant Hermitian structures on Lie groups. We prove that solutions on 2-step nilpotent Lie groups and on almost-abelian Lie groups converge, after a suitable…

In this paper we study the geodesic flow on nilmanifolds equipped with a left-invariant metric. We write the underlying definitions and find general formulas for the Poisson involution. As an example we develop the Heisenberg Lie group…

A von Neumann flow is a special flow over an irrational rotation of the circle and under a piecewise $C^1$ roof function with a non-zero sum of jumps. We prove that the absolute value of the slope is a (measure theoretic) invariant in the…

Using a continuous unitary transformation recently proposed by Wegner \cite{Wegner} together with an approximation that neglects irrelevant contributions, we obtain flow equations for Hamiltonians. These flow equations yield a diagonal or…

We study flows of $G_2$-structures guided by the principle of dimensional reduction: natural geometric flows in $G_2$-geometry reduce to natural flows in complex geometry. Our main examples are the $G_2$-Laplacian coflow, which lifts the…

In the paper we present a generalization to Hamiltonian flows on symplectic manifolds of the estimate proved by Ballmann and Wojtkovski in \cite{BaWoEnGeo} for the dynamical entropy of the geodesic flow on a compact Riemannian manifold of…

Models of geometric flows pertaining to $\mathcal{R}^2$ scale invariant (super) gravity theories coupled to conformally invariant matter fields are investigated. Related to this work are supersymmetric scalar manifolds that are isomorphic…

We analyse second order (in Riemann curvature) geometric flows (un-normalised) on locally homogeneous three manifolds and look for specific features through the solutions (analytic whereever possible, otherwise numerical) of the evolution…

Particles moving inside a fluid near, and interacting with, invariant manifolds is a common phenomenon in a wide variety of applications. One elementary question is whether we can determine once a particle has entered a neighbourhood of an…

We consider a one-parameter family of closed, embedded hypersurfaces moving with normal velocity $G_\kappa = \big ( \sum_{i < j} \frac{1}{\lambda_i+\lambda_j-2\kappa} \big )^{-1}$, where $\lambda_1 \leq \hdots \leq \lambda_n$ denote the…

Let $X$ be a compact Hermitian surface, and $g$ be any fixed Gauduchon metric on $X$. Let $E$ be an Hermitian holomorphic vector bundle over $X$. On the bundle $E$, Donaldson's heat flow is gauge equivalent to a flow of holomorphic…