Related papers: Measure rigidity of Anosov flows via the factoriza…
We prove dynamical stability and instability theorems for compact Einstein metrics under the Ricci flow. We give a nearly complete charactarization of dynamical stability and instability in terms of the conformal Yamabe invariant and the…
We study (topological) pseudo-Anosov flows from the perspective of the associated group actions on their orbit spaces and boundary at infinity. We extend the definition of Anosov-like action from [BFM22] from the transitive to the general…
We give a new proof of a result by Fathi, which states that, to any homeomorphism of a closed surface which is isotopic to a pseudo-Anosov homeomorphism, we can associate a stable and an unstable invariant partition of the surface with…
We analyze a class of deformations of Anosov diffeomorphisms: these $C^0$-small, but $C^1$-macroscopic deformations break the topological conjugacy class but leave the high entropy dynamics unchanged. More precisely, there is a partial…
A consistent framework has been put forward to quantize the isentropic, compressible and inviscid fluid model in the Hamiltonian framework, using the Clebsch parameterization. The naive quantization is hampered by the non-canonical (in…
We investigate the relevance of the conformal method by investigating stability issues for the Einstein-Lichnerowicz conformal constraint system in a nonlinear scalar-field setting. We prove the stability of the system with respect to…
In this paper, we report several new geometric and Lyapunov characterizations of incrementally stable systems on Finsler and Riemannian manifolds. A new and intrinsic proof of an important theorem in contraction analysis is given via the…
We study the quantization of abelian gauge theories of principal torus bundles over compact manifolds with and without boundary. It is shown that these gauge theories suffer from a Gribov ambiguity originating in the non-triviality of the…
Our review covers microscopic foundations of generalized hydrodynamics (GHD). As one generic approach we develop form factor expansions, for ground states and generalized Gibbs ensembles (GGE). In the latter case the so obtained results are…
This article is a sequel to the book `Ricci Flow and the Poincare Conjecture' by the same authors. Using the main results of that book we establish the Geometrization Conjecture for all compact, orientable three-manifolds following the…
We present a new, stable, mixed finite element (FE) method for linear elastostatics of nearly incompressible solids. The method is the automatic variationally stable FE (AVS-FE) method of Calo, Romkes and Valseth, in which we consider a…
In this work we address the problem of existence and uniqueness (finiteness) of ergodic equilibrium states for partially hyperbolic diffeomorphisms isotopic to Anosov on $\mathbb{T}^4$, with 2-dimensional center foliation. To do so we…
Algorithms for studying transitions and instabilities in incompressible flows typically require the solution of linear systems with the full Jacobian matrix. Other popular approaches, like gradient-based design optimization and fully…
We develop a model-theoretic framework for the study of distal factors of strongly ergodic, measure-preserving dynamical systems of countable groups. Our main result is that all such factors are contained in the (existential) algebraic…
We prove a rigidity result for group actions on the line whose elements have what we call "hyperbolic-like" dynamics. Using this, we give a spectral rigidity theorem for $\mathbb{R}$-covered Anosov flows on 3-manifolds, characterizing orbit…
This paper is devoted to rigidity results for some elliptic PDEs and related interpolation inequalities of Sobolev type on smooth compact connected Riemannian manifolds without boundaries. Rigidity means that the PDE has no other solution…
We study the relationship between the Lyapunov exponents of the geodesic flow of a closed negatively curved manifold and the geometry of the manifold. We show that if each periodic orbit of the geodesic flow has exactly one Lyapunov…
We modify the conjectural Bogomolov-Gieseker type inequality introduced by Bayer, Macri and Toda to construct a family of geometric Bridgeland stability conditions on smooth projective 3-folds. We give an equivalent conjecture which needs…
A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means…
A phase-field method for unstructured grids that is accurate, conservative, and robust is proposed in this work. The proposed method also results in bounded transport of volume fraction, and the interface thickness adapts automatically to…