Related papers: Sufficient conditions for rescaling expansivity
In this paper, given a compact Kcsc orbifolds of any dimension and with nontrivial holomorphic vector fields, we find sufficient conditions on the position of singular points in order to admit a Kcsc desingularization, generalizing the…
We develop a parabolic pluripotential theory on compact K{\"a}hler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge-Amp{\`e}re equations. We provide a parabolic analogue of the celebrated Bedford-Taylor…
In this paper we prove two backward uniqueness theorems for extrinsic geometric flow of possibly non-compact hypersurfaces in general ambient complete Riemannian manifolds. These are applicable to a wide range of extrinsic geometric flow,…
We study a class of discontinuous vector fields brought to our attention by multi-legged animal locomotion. Such vector fields arise not only in biomechanics, but also in robotics, neuroscience, and electrical engineering, to name a few…
We study the late time evolution of flat and negatively curved FRW models with a perfect fluid matter source and a scalar field having an arbitrary non-negative potential function $V(\phi) .$ We prove using a dynamical systems approach four…
We investigate the integral conditions to extend the mean curvature flow in a Riemannian manifold. We prove that the mean curvature flow solution with finite total mean curvature on a finite time interval $[0,T)$ can be extended over time…
It is still an open problem that a complete open Kahler manifold with positive bisectional curvature is Stein. This paper partially resolve the problem by putting a restriction to volume growth condition. The partial solution here improves…
In this paper we prove that a nonflat K\"{a}hler-Ricci soliton of the Ricci flow on a complex two-dimensional K\"{a}hler manifold with nonnegative holomorphic bisectional curvature can not be of maximal volume growth.
In this paper, we prove that finite-dimensional topological flows without fixed points and having a countable number of periodic orbits, have the small flow boundary property. This enables us to answer positively a question of Bowen and…
We show that the formal alpha' expansion for heterotic flux vacua is only sensible when flux quantization and the appearance of string scale cycles in the geometry are carefully taken into account. We summarize a number of properties of…
We study the virial expansion of mixtures of countably many different types of particles. The main tool is the Lagrange-Good inversion formula, which has other applications such as counting coloured trees or studying probability generating…
We show global existence and convergence results for the pluriclosed flow on manifolds for which certain naturally associated tensor bundles are globally generated.
The main purpose of the paper is to establish a closedness theorem over Henselian valued fields $K$ of equicharacteristic zero (not necessarily algebraically closed) with separated analytic structure. It says that every projection with a…
In this note we generalize an extension theorem in [5] and [9] of the mean curvature flow to the H^{k} mean curvature flow under some extra conditions. The main difficult problem in proving the extension theorem is to find a suitable…
We study two notions of expansiveness for continuous semiflows: expansiveness in the sense of Alves, Carvalho and Siqueira (2017), and an adaptation of positive expansiveness in the sense of Artigue (2014). We prove that if $X$ is a metric…
We show that the general solution of scalar field cosmology in $d$ dimensions with exponential potentials for flat Robertson-Walker metric can be found in a straightforward way by introducing new variables which completely decouple the…
Let $\varphi_t : M \to M$ be a flow on a smooth closed connected manifold $M$ that preserves and expands a foliation $F$. We establish a theorem of propagation of regularity along the leaves of $F$ for sections of vector bundles satisfying…
The periodic orbit conjecture states that, on closed manifolds, the set of lengths of the orbits of a non-vanishing vector field all whose orbits are closed admits an upper bound. This conjecture is known to be false in general due to a…
We demonstrate existence and uniqueness of Picard--Vessiot extensions satisfying prescribed properties, for systems of linear differential equations over a field satisfying the same properties, under some closure assumptions on the field of…
Given a singular Riemannian foliation on a compact Riemannian manifold, we study the mean curvature flow equation with a regular leaf as initial datum. We prove that if the leaves are compact and the mean curvature vector field is basic,…