Related papers: Stability Conditions on $\mathbb P^3$
We prove global wellposedness in the energy space of the defocusing cubic nonlinear Schroedinger and Gross-Pitaevskii equations on the exterior of a non-trapping domain in dimension 3. The main ingredient is a Strichartz estimate obtained…
We reconsider both the global and local stability of solutions of continuously evolving dynamical systems from a geometric perspective. We clarify that an unambiguous definition of stability generally requires the choice of additional…
For each integer $n\geq2$ we describe the space of stability conditions on the derived category of the $n$-dimensional Ginzburg algebra associated to the $A_2$ quiver. The form of our results points to a close relationship between these…
We consider a noncommutative scalar field with a covariantly constant noncommutative parameter in a curved space-time background. For a potential as a noncommutative polynomial it is shown that the stability conditions are unaffected by the…
Using basic properties of one-sided Heegaard splittings, a direct proof that geometrically compressible one-sided splittings of RP^3 are stabilised is given. The argument is modelled on that used by Waldhausen to show that two-sided…
We establish the stability in the energy space for sums of solitons of the one-dimensional Gross-Pitaevskii equation when their speeds are mutually distinct and distinct from zero, and when the solitons are initially well-separated and…
A result due in its various parts to Hendrickson, Connelly, and Jackson and Jord\'an, provides a purely combinatorial characterisation of global rigidity for generic bar-joint frameworks in $\mathbb{R}^2$. The analogous conditions are known…
In this article, we consider the global well-posedness to the 3-D incompressible inhomogeneous Navier-Stokes equations with a class of large velocity. More precisely, assuming $a_0 \in \dot{B}_{q,1}^{\frac{3}{q}}(\mathbb{R}^3)$ and…
A system of three particles undergoing inelastic collisions in arbitrary spatial dimensions is studied with the aim of establishing the domain of ``inelastic collapse''---an infinite number of collisions which take place in a finite time.…
The well-posedness of the three dimensional Prandtl equation is an outstanding open problem due to the appearance of the secondary flow even though there are studies on analytic and Gevrey function spaces. This problem is raised as the…
We apply a conjectured inequality on third chern classes of stable two-term complexes on threefolds to Fujita's conjecture. More precisely, the inequality is shown to imply a Reider-type theorem in dimension three which in turn implies that…
In this article, we show that some semi-rigid $\mu$-stable sheaves on a projective K3 surface $X$ with Picard number 1 are stable in the sense of Bridgeland's stability condition. As a consequence of our work, we show that the special set…
The stability requirements for a noncommutative scalar field coupled to gravity is investigated through the positive energy theorem. It is shown that for a noncommutative scalar with a polynomial potential, the stability conditions are…
The global well-posedness for the incompressible Navier-Stokes-Vlasov equations in two spatial dimensions is established by a priori estimates, the characteristic method and the semigroup analysis.
We show that the stability conditions on the Kuznetsov component of a Gushel-Mukai threefold, constructed by Bayer, Lahoz, Macr\`i and Stellari, are preserved by the Serre functor, up to the action of the universal cover of…
We prove some positivity results on the coefficients in the complexified Hilbert polynomial of a semi-stable object. After applying these results on the classical slope stability conditions, we get sequences of quadratic inequalities for…
We study the canonical stability index of nonsingular projective varieties of general type with either large canonical volume or large geometric genus. As applications of a general extension theorem established in the first part, we prove…
This paper deals with uniform stabilization of the damped wave equation. When the manifold is compact and the damping is continuous, the geometric control condition is known to be necessary and sufficient. In the case where the damping is a…
Let the complexity of a closed manifold M be the minimal number of simplices in a triangulation of M. Such a quantity is clearly submultiplicative with respect to finite coverings, and by taking the infimum on all finite coverings of M…
In this paper, we prove that the systolic volume of a closed aspherical 3-manifold is bounded below in terms of complexity. Systolic volume is defined as the optimal constant in a systolic inequality. Babenko showed that the systolic volume…