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19952026
most citedInverse Problem for a Curved Quantum Guide

1k citations

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80 papers · 1 filter

math.CV2025

The affine geometry of meromorphic connections with irregular singularities

Xavier Buff, Arnaud Chéritat, Guillaume Tahar

A meromorphic connection on the tangent bundle of a Riemann surface induces a complex affine structure on the complement of the poles. Local models for Fuchsian singularities are a…

math.CV2025

A new approach to the Monge-Ampère eigenvalue problem

Chinh H. Lu, Ahmed Zeriahi

We study the eigenvalue problem for the complex Monge-Ampère operator in bounded hyperconvex domains in $\C^n$, where the right-hand side is a non-pluripolar positive Borel measure…

math.CV2025

Optimal bounds for the Kobayashi distance near -smooth boundary points

Nikolai Nikolov, Pascal J. Thomas

It is shown that the optimal upper and lower bounds for the Kobayashi distance near -smooth strongly pseudoconvex boundary points obtained in L. Kosinski, N. Niko…

math.CV2024

Zalcman's lemma, Pinchuk's rescaling method, and Catlin's estimates revisited

François Berteloot

We present a renormalization lemma for certain maps defined on the unit disc of C and taking values in some metric space. We show that the classical renormalization lemmas of Zalcm…

math.CV2024

Visible -smooth domains are pseudoconvex

Nikolai Nikolov, Ahmed Yekta Ökten, Pascal J. Thomas

We show that a domain that satisfies the visibility property with -smooth boundary is pseudoconvex.

math.CV2024

Kähler families of Green's functions

Vincent Guedj, Tat Dat Tô

In a remarkable series of works, Guo, Phong, Song, and Sturm have obtained key uniform estimates for the Green's functions associated with certain Kähler metrics. In this note, we…