Related papers: Boundary points, minimal $L^2$ integrals and conca…

In this article, we consider a modified version of minimal $L^2$ integrals on sublevel sets of plurisubharmonic functions related to modules at boundary points, and obtain a concavity property of the modified version. As an application, we…

In this article, we present characterizations of the concavity property of minimal $L^2$ integrals degenerating to linearity in the case of fibrations over products of open Riemann surfaces. As applications, we obtain characterizations of…

In this article, we present characterizations of the concavity property of minimal $L^2$ integrals degenerating to linearity in the case of fibrations over open Riemann surfaces. As applications, we obtain characterizations of the holding…

In this article, we consider minimal $L^2$ integrals on the sublevel sets of plurisubharmonic functions on weakly pseudoconvex K\"ahler manifolds with Lebesgue measurable gain related to modules at boundary points of the sublevel sets, and…

In this article, we present characterizations of the concavity property of minimal $L^2$ integrals with negligible weights degenerating to linearity on the fibrations over open Riemann surfaces and the fibrations over products of open…

In this article, we give some necessary conditions for the concavity property of minimal $L^2$ integrals degenerating to partial linearity, a charaterization for the concavity degenerating to partial linearity for open Riemann surfaces, and…

In this article, for singular hermitian metrics on holomorphic vector bundles, we consider minimal $L^2$ integrals on sublevel sets of plurisubharmonic functions on weakly pseudoconvex K\"ahler manifolds related to modules at boundary…

In this article, we present a characterization of the concavity property of minimal $L^2$ integrals degenerating to linearity in the case of finite points on open Riemann surfaces. As an application, we give a characterization of the…

In this article, we present a concavity property of the minimal $L^2$ integrals related to multiplier ideal sheaves with Lebesgue measurable gain. As applications, we give necessary conditions for our concavity degenerating to linearity,…

In this article, we present characterizations of the concavity property of minimal $L^2$ integrals degenerating to linearity in the case of products of analytic subsets on products of open Riemann surfaces. As applications, we obtain…

In this article, we present a concavity property of the minimal $L^{2}$ integrals related to multiplier ideal sheaves with Lebesgue measurable gain on weakly pseudoconvex K\"ahler manifolds. As applications, we give a necessary condition…

In this note, we present the concavity of the minimal $L^2$ integrals related to multiplier ideals sheaves on Stein manifolds. As applications, we obtain a necessary condition for the concavity degenerating to linearity, a characterization…

In this note, we present a general version of the concavity of the minimal $L^{2}$ integrals related to multiplier ideal sheaves.

In this article, we consider Bergman kernels with respect to modules at boundary points, and obtain a log-subharmonicity property of the Bergman kernels, which deduces a concavity property related to the Bergman kernels. As applications, we…

In this article, we consider Bergman kernels related to modules at boundary points on Stein manifolds, and obtain a log-subharmonicity property of the Bergman kernels. As applications, we obtain a lower estimate of weighted $L^2$ integrals…

We prove a local rigidity result for infinitesimally rigid capillary surfaces in some Riemannian $3$-manifolds with mean convex boundary. We also derive bounds on the genus, number of boundary components and area of any compact two-sided…

We study the moduli space of logarithmic connections of rank 2 on the Riemann sphere minus n points with fixed spectral data. There are two natural Lagrangian maps: one towards apparent singularities of the associated fuchsian scalar…

Let $L$ be a special Lagrangian submanifold of a compact, Calabi-Yau manifold $M$ with boundary lying on the symplectic, codimension 2 submanifold $W$. It is shown how deformations of $L$ which keep the boundary of $L$ confined to $W$ can…

In this article, we consider the minimal $L^2$ integrals for the Hardy spaces and the Bergman spaces, and we present some relations between them, which can be regarded as the solutions of the finite points versions of Saitoh's conjecture…

For the purpose of proving the strong openness conjecture of multiplier ideal sheaves, Jonsson-Musta\c{t}\u{a} posed an enhanced conjecture and proved the two-dimensional case, which says that: the Lebesgue measure of the set…