Related papers: Stratification of three-dimensional real flows I: …
In this paper we analyze the long-time behaviour of 3 dimensional Ricci flow with surgery. We prove that under the topological condition that the initial manifold only has non-aspherical or hyperbolic components in its geometric…
Landmark manifolds consist of a collection of distinct points, and dynamics on this manifold can be used to represent flows, such as solutions of ODEs and flows deforming a shape. We will consider landmark configurations in the Euclidean…
Given a locally maximal compact invariant hyperbolic set $\Lambda$ for a $C^1$ flow or diffeomorphism on a Riemann manifold with $C^1$ unstable laminations, we construct an invariant continuous bundle of tangent vectors to local unstable…
We prove rigidity results describing contextually-constrained maps defined on Grassmannians and manifolds of ordered independent line tuples in finite-dimensional vector or Hilbert spaces. One statement in the spirit of the Fundamental…
This work is devoted to the study of non-Newtonian fluids of grade three on two-dimensional and three-dimensional bounded domains, driven by a nonlinear multiplicative Wiener noise. More precisely, we establish the existence and uniqueness…
We use Lott's functional and construct a new functional to derive rigidity results for invariant Ricci flow blowdown limits on nilpotent principal bundles with zero associated curvature. Consequently, we prove that the blowdown limit is…
We prove a local minimizing property for strictly stable free-boundary minimal hypersurfaces in the relative current setting. Let $\Sigma^n$ be a compact, two-sided, properly embedded free-boundary minimal hypersurface in a compact…
Strongly coupled field theories with gravity duals can be placed at finite density in two ways: electric field flux emanating from behind a horizon, or bulk charged fields outside of the horizon that explicitly source the density. We…
Over the last 10 years or so, advanced statistical properties, including exponential decay of correlations, have been established for certain classes of singular hyperbolic flows in three dimensions. The results apply in particular to the…
The geometry of a ball within a Riemannian manifold is coarsely controlled if it has a lower bound on its Ricci curvature and a positive lower bound on its volume. We prove that such coarse local geometric control must persist for a…
We study valued fields equipped with an automorphism $\sigma$ which is locally infinitely contracting in the sense that $\alpha\ll\sigma\alpha$ for all $0<\alpha\in\Gamma$. We show that various notions of valuation theory, such as Henselian…
We consider the noncommutative space $\mathbb{R}^3_\lambda$, a deformation of the algebra of functions on $\mathbb{R}^3$ which yields a "foliation" of $\mathbb{R}^3$ into fuzzy spheres. We first construct a natural matrix base adapted to…
We use Ricci flow to obtain a local bi-Holder correspondence between Ricci limit spaces in three dimensions and smooth manifolds. This is more than a complete resolution of the three-dimensional case of the conjecture of…
This paper concerns the structural stability of smooth cylindrically symmetric transonic flows in a concentric cylinder. Both cylindrical and axi-symmetric perturbations are considered. The governing system here is of mixed…
We complete the theoretical framework required for the construction of a Morse homology theory for certain types of forced mean curvature flows. The main result of this paper describes the asymptotic behaviour of these flows as the forcing…
A path-following control algorithm enables a system's trajectories under its guidance to converge to and evolve along a given geometric desired path. There exist various such algorithms, but many of them can only guarantee local convergence…
In his seminal work \cite{Ri96}, Rivin characterized finite ideal polyhedra in three-dimensional hyperbolic space. However, the characterization of infinite ideal polyhedra, as proposed by Rivin, has remained a long-standing open problem.…
A mean curvature flow starting from a closed embedded hypersurface in $R^{n+1}$ must develop singularities. We show that if the flow has only generic singularities, then the space-time singular set is contained in finitely many compact…
On a hyperbolic 3-manifold of finite volume, we prove that if the initial metric is sufficiently close to the hyperbolic metric $h_0$, then the normalized Ricci-DeTurck flow exists for all time and converges exponentially fast to $h_0$ in a…
Magnetized orbifolds play an important role in compactifications of string theories and higher-dimensional field theories to four dimensions. Magnetic flux leads to chiral fermions, it can be a source of supersymmetry breaking and it is an…