相关论文: Sharp $C^{1,\bar1}$ estimates in K\"ahler quantiza…

We study the interplay between the following types of special non-K\"ahler Hermitian metrics on compact complex manifolds: it locally conformally K\"ahler, $k$-Gauduchon, balanced and locally conformally balanced and prove that a locally…

We consider a notion of balanced metrics for triples (X,L,E) which depend on a parameter \alpha, where X is smooth complex manifold with an ample line bundle L and E is a holomorphic vector bundle over X. For generic choice of \alpha, we…

If $f$ is a nonzero Bohr almost periodic function on $\mathbb R$ with a bounded spectrum we prove there exist $C_f > 0$ and integer $n > 0$ such that for every $u > 0$ the mean measure of the set $\{\, x \, : \, |f(x)| < u \, \}$ is less…

Let $\Sigma$ be a $\sigma$-algebra over $\Omega$, and let $M(\Sigma)$ denote the Banach space of complex measures. Consider a representation $T_t$ for $t\in\Bbb R$ acting on $M(\Sigma)$. We show that under certain, very weak hypotheses,…

Let $E\subset \mathbb{R}^{n+1}$, $n\ge 2$, be an Ahlfors-David regular set of dimension $n$. We show that the weak-$A_\infty$ property of harmonic measure, for the open set $\Omega:= \mathbb{R}^{n+1}\setminus E$, implies uniform…

In this paper we will discuss local coordinates canonically corresponding to a Kahler metric. We will also discuss and prove the $C^\infty$ convergence of Bergman metrics following Tian's result on $C^2$ convergence of Bergman metrics. At…

We prove that a sub-Riemannian manifold equipped with a full-support Radon measure is never $\mathrm{CD}(K,N)$ for any $K\in \mathbb{R}$ and $N\in (1,\infty)$ unless it is Riemannian. This generalizes previous non-CD results for…

We show how to build a kernel \[ K_X(x,y)=\sum_{m=0}^Xh(\lambda_m/{\lambda_X})\varphi_m(x)\overline{\varphi_m(y)} \] on a compact Riemannian manifold $M$, which is positive up to a negligible error and such that $K_X(x,x)\approx X$. Here…

We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold $(M,J)$ admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the…

The Fisher information metric or the Fisher-Rao metric corresponds to a natural Riemannian metric defined on a parameterized family of probability density functions. As in the case of Riemannian geometry, we can define a distance in terms…

In this paper we continue our study on the canonical metrics on the Teichm\"uller and the moduli space of Riemman surfaces. We first prove the equivalence of the Bergman metric and the Carath\'eodory metric to the K\"ahler-Einstein metric,…

This paper establishes quantitative high-probability bounds on the eigenvalues and eigenfunctions of $\epsilon$-neighborhood graph Laplacians constructed from i.i.d. random variables on $m$-dimensional closed Riemannian manifolds $(M,g)$…

We prove new Beckner-Sobolev type inequalities on compact K\"{a}hler manifolds with positive Ricci curvature. As an application, we obtain a diameter upper bound that improves the Bonnet-Myers bound.

For a bounded domain $D \subset \mathbb{C}^n$, let $K_D = K_D(z) > 0$ denote the Bergman kernel on the diagonal and consider the reproducing kernel Hilbert space of holomorphic functions on $D$ that are square integrable with respect to the…

We present a systematic collection of results concerning interactions between convex, subharmonic and pluri-subharmonic functions on pairs of manifolds related by a Riemannian submersion. Our results are modelled on those known in the…

We establish a good lambda inequality relating to the distribution function of Riesz potential and fractional maximal function on $\left(\mathbb{R}^n, d\mu\right)$ where $\mu$ is a positive Radon measure which doesn't necessarily satisfy a…

We revisit the measurement of the polarization fraction, $P$, and the measurement of the polarization angle of partially linearly-polarized gamma rays using their conversion to $e^+e^-$ pairs in the field of a nucleus. We show that an…

In this paper we consider the inverse problem of determining on a compact Riemannian manifold the electric potential and the absorption coefficient in the wave equation with Dirichlet data from measured Neumann boundary observations. This…

We extend Tsuji's iterative construction of complete K\"ahler--Einstein metrics with negative scalar curvature to noncompact K\"ahler manifolds with bounded geometry, using Berndtsson's method from the compact setting. Consequently, given a…

We obtain a compactness result for various classes of Riemannian metrics in dimension four; in particular our method applies to anti-self-dual metrics, Kahler metrics with constant scalar curvature, and metrics with harmonic curvature. With…