Related papers: Degenerations of LeBrun twistor spaces
We prove bounds in the strict local $L^{2}(\mathbb{R}^{d})$ range for trilinear Fourier multiplier forms with a $d$-dimensional singular subspace. Given a fixed parameter $K \ge 1$, we treat multipliers with non-degenerate singularity that…
An algebraic restriction of the nonabelian self-dual Chern-Simons-Higgs systems leads to coupled abelian models with interesting mass spectra. The vacua are characterized by embeddings of $SU(2)$ into the gauge algebra, and in the broken…
We show that simply connected toric hyperK\"ahler metrics of finite topological type with maximal volume growth are generically quasi-asymptotically conical, which allows us to compute explicitly their reduced $L^2$-cohomology groups. In…
In joint work with Chen and Weber, the author has elsewhere shown that CP2#2(-CP2) admits an Einstein metric. The present paper gives a new and rather different proof of this fact. Our results include new existence theorems for extremal…
This article is a study guide for ``On restricted projections to planes in $\mathbb R^3$" [arXiv:2207.13844] by Gan, Guo, Guth, Harris, Maldague and Wang. We first present the main problems and preliminaries related to restricted…
For one-parameter degenerations of compact K\"ahler manifolds, we determine the asymptotic behavior of the first Chern form of the direct image of a Nakano semi-positive vector bundle twisted by the relative canonical bundle, when the…
This is a survey of our recent work on degenerations of Ricci-flat Kahler metrics on compact Calabi-Yau manifolds with Kahler classes approaching the boundary of the Kahler cone.
We study general linear perturbations of a class of 4d real-dimensional hyperkahler manifolds obtainable by the (generalized) Legendre transform method. Using twistor methods, we show that deformations can be encoded in a set of holomorphic…
In the present work some examples of toric hyperkahler metrics in eight dimensions are constructed. First it is described how the Calderbank-Pedersen metrics arise as a consequence of the Joyce description of selfdual structures in four…
One way to study the combinatorics of finite metric spaces is to study the betweenness relation associated with the metric space. In the hypergraph metrization problem, one has to find and characterize metric betweennesses whose collinear…
This paper is concerned with the construction of special metrics on non-compact 4-manifolds which arise as resolutions of complex orbifold singularities. Our study is close in spirit to the construction of the hyperkaehler gravitational…
We provide the first explicit examples of deformations of higher dimensional quadrics: a straightforward generalization of Peterson's explicit 1-dimensional family of deformations in $\mathbb{C}^3$ of 2-dimensional general quadrics with…
This paper analyses the convergence and degeneration of sequences of metrics on a 3-manifold, and relations of such with Thurston's geometrization conjecture. The sequences are minimizing sequences for a certain (optimal) scalar-curvature…
We obtain the super-Landau-Ginzburg mirror of the A-twisted topological sigma model on a twistor superspace -- the quadric in CP^{3|3} x CP^{3|3} which is a Calabi-Yau supermanifold. We show that the B-model mirror has a geometric…
We determine the group of conformal automorphisms of the self-dual metrics on n#CP^2 due to LeBrun for n>2, and Poon for n=2. These metrics arise from an ansatz involving a circle bundle over hyperbolic three-space H^3 minus a finite number…
The aim of this paper is to present examples of Kahler holomorphically pseudosymmetric metrics on the projective space CP^n.
A purely combinatorial compactification of the configuration space of n (>4) distinct points with equal weights in the real projective line was introduced by M. Yoshida. We geometrize it so that it will be a real hyperbolic cone-manifold of…
We study a class of limits of the higher-dimensional Kerr-NUT-(A)dS spacetimes where particular roots of metric functions degenerate. Namely, we obtain the Taub-NUT-(A)dS and the extreme near-horizon geometries as two examples of our…
The decay $K_L\rightarrow \pi^o\nu\overline{\nu}$ is an excellent probe of the nature of CP violation. It is almost entirely CP-violating, and hadronic uncertainties are negligible. Experiments which hope to detect the decay are currently…
We study the algebraic dimension a(X) of a compact hyperkaehler manfold of dimension 2n. We show that a(X) is at most n unless X is projective. If a compact Kaehler manifold with algebraic dimension 0 and Kodaira dimension 0 has a minimal…