Complex Variables

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New submissions for Tue, 14 May 24

[1]  arXiv:2405.07261 [pdf, ps, other]

Title: A Le Potier-type isomorphism twisted with multiplier submodule sheaves

Authors: Yaxiong Liu, Zhuo Liu, Hui Yang, Xiangyu Zhou

Subjects: Complex Variables (math.CV)

In this paper, we obtain a Le Potier-type isomorphism theorem twisted with multiplier submodule sheaves, which relates a holomorphic vector bundle endowed with a strongly Nakano semipositive singular Hermitian metric to the tautological line bundle with the induced metric. As applications, we obtain a Koll\'ar-type injectivity theorem, a Nadel-type vanishing theorem, and a singular holomorphic Morse inequality for holomorphic vector bundles and so on.

[2]  arXiv:2405.07618 [pdf, ps, other]

Title: Toeplitz Operators and Berezin-type Operators on Different Bergman Spaces

Authors: Lvchang Li, Haichou Li

Comments: arXiv admin note: text overlap with arXiv:2404.16439

Subjects: Complex Variables (math.CV); Functional Analysis (math.FA)

In the present paper, we study the boundedness and compactness of Toeplitz operators and Berezin-type operators between different weighted Bergman spaces over tubular domains in $\mathbb{C}^n$. We establish their connection with Carleson measures and provide some characterizations.

[3]  arXiv:2405.07683 [pdf, ps, other]

Title: Integral means spectrum functionals on Teichmüller spaces

Authors: Jianjun Jin

Comments: 24 pages

Subjects: Complex Variables (math.CV)

In this paper, we introduce and study the integral means spectrum (IMS) functionals on Teichm\"uller spaces. We show that the IMS functionals on the closure of the universal Teichm\"uller space and on the asymptotic universal Teichm\"uller space are both continuous. During the proof, we obtain some new results about the universal asymptotic Teichm\"uller space.

[4]  arXiv:2405.07786 [pdf, ps, other]

Title: Analyticity theorems for parameter-dependent plurisubharmonic functions

Authors: Bojie He

Comments: 29 pages, to appear in Mathematica Scandinavica (2024). All comments are welcome!

Subjects: Complex Variables (math.CV); Algebraic Geometry (math.AG)

In this paper, we first show that a union of upper-level sets associated to fibrewise Lelong numbers of plurisubharmonic functions is in general a pluripolar subset. Then we obtain analyticity theorems for a union of sub-level sets associated to fibrewise complex singularity exponents of some special (quasi-)plurisubharmonic functions. As a corollary, we confirm that, under certain conditions, the logarithmic poles of relative Bergman kernels form an analytic subset when the (quasi-)plurisubharmonic weight function has analytic singularities. In the end, we give counterexamples to show that the aforementioned sets are in general non-analytic even if the plurisubharmonic function is supposed to be continuous.

Cross-lists for Tue, 14 May 24

[5]  arXiv:2405.07016 (cross-list from math.FA) [pdf, ps, other]

Title: Generalized de Branges-Rovnyak spaces

Authors: Alexandru Aleman, Frej Dahlin

Subjects: Functional Analysis (math.FA); Complex Variables (math.CV)

Given the reproducing kernel $k$ of the Hilbert space $\mathcal{H}_k$ we study spaces $\mathcal{H}_k(b)$ whose reproducing kernel has the form $k(1-bb^*)$, where $b$ is a row-contraction on $\mathcal{H}_k$. In terms of reproducing kernels this it the most far-reaching generalization of the classical de Branges-Rovnyaks spaces, as well as their very recent generalization to several variables. This includes the so called sub-Bergman spaces in one or several variables. We study some general properties of $\mathcal{H}_k(b)$ e.g. when the inclusion map into $\mathcal{H}$ is compact. Our main result provides a model for $\mathcal{H}_k(b)$ reminiscent of the Sz.-Nagy-Foia\c{s} model for contractions. As an application we obtain sufficient conditions for the containment and density of the linear span of $\{k_w:w\in\mathcal{X}\}$ in $\mathcal{H}_k(b)$. In the standard cases this reduces to containment and density of polynomials. These methods resolve a very recent conjecture regarding polynomial approximation in spaces with kernel $\frac{(1-b(z)b(w)^*)^m}{(1-z\overline w)^\beta}, 1\leq m<\beta, m\in\mathbb{N}$.

[6]  arXiv:2405.07082 (cross-list from math.PR) [pdf, other]

Title: Commutation relations for two-sided radial SLE

Authors: Yilin Wang, Hao Wu

Comments: 40 pages, 5 figures

Subjects: Probability (math.PR); Complex Variables (math.CV)

We study the commutation relation for 2-radial SLE in the unit disc starting from two boundary points. We follow the framework introduced by Dub\'{e}dat. Under an additional requirement of the interchangeability of the two curves, we classify all locally commuting 2-radial SLE$_\kappa$ for $\kappa\in (0,4]$: it is either a two-sided radial SLE$_\kappa$ with spiral of constant spiraling rate or a chordal SLE$_\kappa$ weighted by a power of the conformal radius of its complement. Namely, for fixed $\kappa$ and starting points, we have exactly two one-parameter continuous families of locally commuting 2-radial SLE. Two-sided radial SLE with spiral is a generalization of two-sided radial SLE (without spiral) which satisfies the resampling property. We define it by weighting two independent radial SLEs by a two-time parameter martingale. However, unlike in the chordal case, the resampling property does not uniquely determine the pair due to the additional degree of freedom in the spiraling rate. We also discuss the semiclassical limit of the commutation relation as $\kappa \to 0$.

[7]  arXiv:2405.07929 (cross-list from math.AP) [pdf, ps, other]

Title: On the Smooth Curve of Entire Vector Fields that Solves the Navier-Stokes Equation

Authors: Brian David Vasquez Campos

Subjects: Analysis of PDEs (math.AP); Complex Variables (math.CV); Functional Analysis (math.FA)

In this paper we prove the existence and smoothness of the Navier-Stokes Equation for viscosity large enough which after rescaling implies a solution for any positive viscosity, additionally, we show the existence of a curve of entire vector fields of order 2 that extends the solution to the complex domain for positive time.

[8]  arXiv:2405.07936 (cross-list from math.AG) [pdf, ps, other]

Title: A Perspective on the Foundations of Derived Analytic Geometry

Authors: Oren Ben-Bassat, Jack Kelly, Kobi Kremnizer

Comments: Comments and feedback very welcome; 274 pages

Subjects: Algebraic Geometry (math.AG); Algebraic Topology (math.AT); Complex Variables (math.CV); Number Theory (math.NT)

We show how one can do algebraic geometry with respect to the category of simplicial objects in an exact category. As a biproduct, we get a theory of derived analytic geometry.

Replacements for Tue, 14 May 24

[9]  arXiv:2204.04945 (replaced) [pdf, ps, other]

Title: Linearization of transition functions along a certain class of Levi-flat hypersurfaces

Authors: Satoshi Ogawa

Comments: 18 pages

Subjects: Complex Variables (math.CV); Dynamical Systems (math.DS)

[10]  arXiv:2208.14327 (replaced) [pdf, ps, other]

Title: Some interesting birational morphisms of smooth affine quadric $3$-folds

Authors: Cinzia Bisi, Jonathan D. Hauenstein, Tuyen Trung Truong

Comments: 30 pages. A revised version

Journal-ref: Nonlinearity, 2024

Subjects: Algebraic Geometry (math.AG); Complex Variables (math.CV); Dynamical Systems (math.DS); Numerical Analysis (math.NA)

[11]  arXiv:2309.03849 (replaced) [pdf, ps, other]

Title: Demystifying the Karpelevic theorem

Authors: Devon N. Munger, Andrew L. Nickerson, Pietro Paparella

Subjects: Spectral Theory (math.SP); Complex Variables (math.CV)

[12]  arXiv:2310.19473 (replaced) [pdf, ps, other]

Title: Wetzel families and the continuum

Authors: Jonathan Schilhan, Thilo Weinert

Comments: 24 pages

Subjects: Logic (math.LO); Complex Variables (math.CV)

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