Related papers: Generalized Kahler Taub-NUTs and Two Exceptional I…
Various curvature conditions are studied on metrics admitting a symmetry group. We begin by examining a method of diagonalizing cohomogeneity-one Einstein manifolds and determine when this method can and cannot be used. Examples, including…
The generalized, two-component Hunter-Saxton system comprises several well-known models of fluid dynamics and serves as a tool for the study of one-dimensional fluid convection and stretching. In this article a general representation…
We extend the arguments of Tosatti-Zhang to reduce a well-known conjecture concerning the structure of the Gromov-Hausdorff limit in both the setting of degenerating Calabi-Yau manifolds and the K\"ahler-Ricci flow to a certain partial…
This paper is concerned with the compactness of metrics of the disk with prescribed Gaussian and geodesic curvatures. We consider a blowing-up sequence of metrics and give a precise description of its asymptotic behavior. In particular, the…
An introduction is provided to some current research trends in stability in geometric invariant theory and the problem of Kaehler metrics of constant scalar curvature. Besides classical notions such as Chow-Mumford stability, the emphasis…
We prove existence of twisted K\"ahler-Einstein metrics in big cohomology classes, using a divisorial stability condition. In particular, when $-K_X$ is big, we obtain a uniform Yau-Tian-Donaldson existence theorem for K\"ahler-Einstein…
This is a continuation of the work of Arezzo-Pacard-Singer and the author on blowups of extremal K\"ahler manifolds. We prove the conjecture stated in [32], and we relate this result to the K-stability of blown up manifolds. As an…
In this paper, by generalizing the concept of balanced metrics, we shall show that Donaldson's asymptotic approximation of balanced metrics for constant scalar curvature cases can be generalized to extremal Kaehler cases.
An asymptotic formula for the Tian-Paul CM-line of a flat family blown-up at a flat closed sub-scheme is given. As an application we prove that the blow-up of a polarized manifold along a (relatively) Chow-unstable submanifold admits no…
In this paper we exhibit a one-parameter family of new Taub-NUT instantons parameterized by a half-line. The endpoint of the half-line will be the reducible Yang-Mills instanton corresponding to the Eguchi-Hanson-Gibbons L^2 harmonic…
The multi-centre metrics are a family of euclidean solutions of the empty space Einstein equations with self-dual curvature. For this full class, we determine which metrics do exhibit an extra conserved quantity quadraic in the momenta,…
Using quantization techniques, we show that the $\delta$-invariant of Fujita-Odaka coincides with the optimal exponent in certain Moser-Trudinger type inequality. Consequently we obtain a uniform Yau-Tian-Donaldson theorem for the existence…
We study Einstein deformations of negative K\"ahler Einstein metrics. We relate the second order Einstein deformation theory of negative K\"ahler-Einstein metrics to the complex geometry of the underlying K\"ahler manifold. After suitable…
We prove a Beale-Kato-Majda type criterion for the loss of regularity for solutions of the incompressible Euler equations in $H^{s}({\mathbb R}^3)$, for $s>\frac52$. Instead of double exponential estimates of Beale-Kato-Majda type, we…
This paper is concerned with the existence of constant scalar curvature Kaehler metrics on blow ups at finitely many points of compact manifolds which already carry constant scalar curvature Kaehler metrics. We also consider the…
A theorem of E.Lerman and S.Tolman, generalizing a result of T.Delzant, states that compact symplectic toric orbifolds are classified by their moment polytopes, together with a positive integer label attached to each of their facets. In…
Several Einstein-Sasaki 7-metrics appearing in the physical literature are fibered over four dimensional Kahler-Einstein metrics. Instead we consider here the natural Kahler-Einstein metrics defined over the twistor space Z of any…
We discuss various aspects of multi-instanton configurations in generic multi-cut matrix models. Explicit formulae are presented in the two-cut case and, in particular, we obtain general formulae for multi-instanton amplitudes in the…
We construct a family of K\"ahler-Einstein edge metrics on all Hirzebruch surfaces using the Calabi ansatz and study their angle deformation. This allows us to verify in some special cases a conjecture of Cheltsov-Rubinstein that predicts…
We consider a class of axially symmetric solutions to Einstein's equations incorporating a $\theta$-dependent scalar field and extend these solutions by introducing electric and magnetic charges via Harrison transformations. Subsequently,…