Related papers: Short-time existence for some higher-order geometr…

We develop a compactness theory for super Ricci flows, which lays the foundations for the partial regularity theory in [Bam20b]. Our results imply that any sequence of super Ricci flows of the same dimension that is pointed in an…

We investigate the properties of the combinatorial Ricci flow for surfaces, both forward and backward -- existence, uniqueness and singularities formation. We show that the positive results that exist for the smooth Ricci flow also hold for…

We study time- and parameter-dependent ordinary differential equations in the geometric setting of vector fields and their flows. Various degrees of regularities in state are considered, including Lipschitz, finitely diferentiable, smooth,…

We consider the general K\"ahler-Ricci flows which exist for all time. The zeroth order control on the flow metric potential for various infinite time singularities is the focus. The possible semi-amplness for numerically effective classes…

The recently developed theory of Lagrangian flows for transport equations with low regularity coefficients enables to consider non BV vector fields. We apply this theory to prove existence and stability of global Lagrangian solutions to the…

A compactness framework is established for approximate solutions to subsonic-sonic flows governed by the steady full Euler equations for compressible fluids in arbitrary dimension. The existing compactness frameworks for the two-dimensional…

We introduce a new geometric flow called the chord shortening flow which is the negative gradient flow for the length functional on the space of chords with end points lying on a fixed submanifold in Euclidean space. As an application, we…

The Weinstein conjecture, as the general existence problem for periodic orbits of Hamiltonian or Reeb flows, has been among the central questions in symplectic topology for over two decades and its investigation has led to understanding of…

In this paper we prove local existence of a Ricci de Turck flow starting at a space with incomplete edge singularities and flowing for a short time within a class of incomplete edge manifolds. We derive regularity properties for the…

In this paper we introduce and study a new kind of hyperbolic geometric flows --dissipative hyperbolic geometric flow. This kind of flow is defined by a system of quasilinear wave equations with dissipative terms. Some interesting exact…

We present a direct derivation of the typical time derivatives used in a continuum description of complex fluid flows, harnessing the principles of the kinematics of line elements. The evolution of the microstructural conformation tensor in…

In this paper, we study the global existence of steady subsonic Euler flows through infinitely long nozzles which are periodic in $x_1$ direction with the period $L$. It is shown that when the variation of Bernoulli function at some given…

We study a class of fourth order curvature flows on a compact Riemannian manifold, which includes the gradient flows of a number of quadratic geometric functionals, as for instance the L2 norm of the curvature. Such flows can develop a…

In this survey paper, I discuss some recent progress on the existence and regularity of Brakke flows. These include: an "end-time version" of Brakke's local regularity theorem, which allows to extend the validity of the celebrated…

We are interested in existence of gradient flows for shape functionals especially for first Laplacian eigenvalues. We introduce different techniques to prove existence and use different formulations for gradient flows. We apply a…

We establish a weak compactness theorem for the moduli space of closed Ricci flows with uniformly bounded entropy, each equipped with a natural spacetime distance, under pointed Gromov-Hausdorff convergence. Furthermore, we develop a…

We study the long time behaviour of Ricci flow with bubbling-off on a possibly noncompact $3$-manifold of finite volume whose universal cover has bounded geometry. As an application, we give a Ricci flow proof of Thurston's hyperbolisation…

For each $n\ge 3$, we construct a 'pancake-like', $O(2)\times O(n-1)$-invariant ancient Ricci flow with positive curvature operator and bounded "girth", and we determine its asymptotic limits backwards in time. This solution is new even in…

The Bach tensor and a vector which generates conformal symmetries allow a conserved four-current to be defined. The Bach four-current gives rise to a quasilocal two-surface expression for power per luminosity distance in the Vaidya exterior…

In this paper we prove a compactness result for Ricci flows with bounded scalar curvature and entropy. It states that given any sequence of such Ricci flows, we can pass to a subsequence that converges to a metric space which is smooth away…