Related papers: Lectures on Stability and Constant Scalar Curvatur…
A mathematical model describing motion of an inhomogeneous incompressible fluid in a Hele-Shaw cell is considered. Linear stability analysis of shear flow class is provided. The role of inertia, linear friction and impermeable boundaries in…
We introduce equations for special metrics, and notions of stability for some new types of augmented holomorphic bundles. These new examples include holomorphic extensions, and in this case we prove a Hitchin-Kobayashi correspondence…
Using dynamical stability of symplectic curvature flow, we show that on a compact Calabi-Yau manifold, any small symplectic deformation of a K\"ahler form remains K\"ahler.
We introduce an analogue of Bridgeland's stability conditions for polarised varieties. Much as Bridgeland stability is modelled on slope stability of coherent sheaves, our notion of Z-stability is modelled on the notion of K-stability of…
We consider two interesting spaces associated to a quiver with potential: a space of stability conditions and a cluster variety. In the case where the quiver with potential arises from an ideal triangulation of a marked bordered surface, we…
Modified gravity theories have received increased attention lately to understand the late time acceleration of the universe. This viewpoint essentially modifies the geometric components of the universe. Among numerous extension to…
We study Hermitian metrics with constant second scalar curvature on compact manifolds. We first consider a Yamabe-type problem for the second Bismut scalar curvature under a natural topological condition, and then analyze elliptic equations…
We investigate the scalar field dynamics of models with nonminimally coupled scalar fields in the presence of the Gauss-Bonnet term and derive the structure of the effective potential and conditions for stable de Sitter solutions in…
We introduce the $G$-stable rank of a higher order tensors over perfect fields. The $G$-stable rank is related to the Hilbert-Mumford criterion for stability in Geometric Invariant Theory. We will relate the $G$-stable rank to the tensor…
Classical gravity coupled to a CFT$_4$ (matter) is considered. The effect of the quantum dynamics of matter on gravity is studied around maximally symmetric spaces (flat, de Sitter and Anti de Sitter). The structure of the graviton…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
Let X be a Fano manifold. G.Tian proves that if X admits a Kaehler-Einstein metric, then it satisfies two different stability conditions: one involving the Futaki invariant of a special degeneration of X, the other Hilbert-Mumford-stability…
In this thesis we study the principle that extremal objects in differential geometry correspond to stable objects in algebraic geometry. In our introduction we survey the most famous instances of this principle with a view towards the…
A stability analysis of a spherically symmetric star in scalar-tensor theories of gravity is given in terms of the frequencies of quasi-normal modes. The scalar-tensor theories have a scalar field which is related to gravitation. There is…
In this paper, we prove that K\"ahler-Ricci flow converges to a K\"ahler-Einstein metric (or a K\"ahler-Ricci soliton) in the sense of Cheeger-Gromov as long as an initial K\"ahler metric is very closed to $g_{KE}$ (or $g_{KS}$) if a…
We prove that the K-moduli space of cubic fourfolds is identical to their GIT moduli space. More precisely, the K-(semi/poly)stability of cubic fourfolds coincide to the corresponding GIT stabilities, which was studied in detail by Laza. In…
In this paper we continue our study about the existence of Kaehler metrics of constant scalar curvature (Kcsc) on blow ups at points of compact manifolds with Kcsc metrics started in math.DG/0411522. In this second part we deal with the…
In this paper we study K-polystability of arbitrary (possibly non-projective) compact K\"ahler manifolds admitting holomorphic vector fields. As a main result, we show that existence of a constant scalar curvature K\"ahler (cscK) metric…
We study the equal-mass classical three rotor problem, a variant of the three body problem of celestial mechanics. The quantum $N$-rotor problem has been used to model chains of coupled Josephson junctions and also arises via a partial…
Three-dimensional direct numerical simulations of an incompressible open square cavity flow are conducted. Features of the permanent (non-linear) regime together with the linear stability analysis of a two-dimensional steady base flow are…