相关论文: Extremal metrics and K-stability (PhD thesis)

We study stability properties of $f$-minimal hypersurfaces isometrically immersed in weighted manifolds with non-negative Bakry-Emery Ricci curvature under volume growth conditions. Moreover, exploiting a weighted version of a finiteness…

We give a moment map interpretation of some relatively balanced metrics. As an application, we extend a result of S. K. Donaldson on constant scalar curvature K\"ahler metrics to the case of extremal metrics. Namely, we show that a given…

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…

Motivated by recent work we study rotating ellipsoidal membranes in the framework of the light-cone supermembrane theory. We investigate stability properties of these classical solutions which are important for the quantization of super…

This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise liner functions recently obtained in [1]. We mainly focus here on establishing relationships between full stability of…

We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…

We prove an equivariant version of the CM minimization conjecture for extremal K\"ahler manifolds. This involves proving that, given an equivariant punctured family of polarized varieties, a relative version of the CM degree is strictly…

Using log canonical thresholds and basis divisors Fujita--Odaka introduced purely algebro-geometric invariants $\delta_m$ whose limit in $m$ is now known to characterize uniform K-stability on a Fano variety. As shown by Blum-Jonsson this…

We study the destabilization of a shear layer, produced by differential rotation of a rotating axisymmetric container. For small forcing, this produces a shear layer, which has been studied by Stewartson and is almost invariant along the…

We introduce a notion of stability for sheaves with respect to several polarisations that generalises the usual notion of Gieseker-stability. We prove, under a boundedness assumption, which we show to hold on threefolds or for rank two…

In the present paper and the companion paper [9] a probabilistic (statistical-mechanical) approach to the construction of canonical metrics on a complex algebraic varieties X is introduced, by sampling "temperature deformed" determinantal…

We propose a new approach to the existence of constant transversal scalar curvature Sasaki structures drawing on ideas and tools from the CR Yamabe problem, establishing a link between the CR Yamabe invariant, the existence of Sasaki…

We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…

The first result in this study is a non-existence theorem for $\alpha-$harmonic mappings. Additionally, a direct connection between the $\alpha-$ harmonic and harmonic maps is made possible via conformal deformation. Second, the instability…

We formulate an effective variant of the Yau-Tian-Donaldson conjecture, then review effective results on K-stability of spherical varieties, that is, K-stability criterions which can be effectively computed given the combinatorial data…

We study the stability of compact pseudo-K\"ahler manifolds, i.e. compact complex manifolds $X$ endowed with a symplectic form compatible with the complex structure of $X$. When the corresponding metric is positive-definite, $X$ is K\"ahler…

We establish an equivalence between conformally Einstein--Maxwell Kahler 4-manifolds (recently studied in many works) and extremal Kahler 4-manifolds (in the sense of Calabi) with nowhere vanishing scalar curvature. The corresponding pairs…

We identify the difference between the CM polarisation and the Chow polarisation on the ``Hilbert scheme''. As a consequence, we give a numerical criterion for the CM stability as in Mumfords' G.I.T.. Also, we write down an explicit formula…

The various scalar curvatures on an almost Hermitian manifold are studied, in particular with respect to conformal variations. We show several integrability theorems, which state that two of these can only agree in the K\"ahler case. Our…

Many classical results in algebraic geometry arise from investigating some extremal behaviors that appear among projective varieties not lying on any hypersurface of fixed degree. We study two numerical invariants attached to such…