HOMOGENIZATION OF RANDOM QUASICONFORMAL MAPPINGS AND RANDOM DELAUNEY TRIANGULATIONS

Oleg Ivrii; Vladimir Marković

doi:https://doi.org/10.4310/jdg/1689262063

HOMOGENIZATION OF RANDOM QUASICONFORMAL MAPPINGS AND RANDOM DELAUNEY TRIANGULATIONS

Oleg Ivrii, Vladimir Marković

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we solve two problems dealing with the homogenization of random media. We show that a random quasiconformal mapping is close to an affine mapping, while a circle packing of a random Delauney triangulation is close to a conformal map, confirming a conjecture of K. Stephenson. We also show that on a Riemann surface equipped with a conformal metric, a random Delauney triangulation is close to being circle packed.

Original language	English
Pages (from-to)	523-551
Number of pages	29
Journal	Journal of Differential Geometry
Volume	124
Issue number	3
DOIs	https://doi.org/10.4310/jdg/1689262063
State	Published - Jul 2023

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Geometry and Topology

Access to Document

https://doi.org/10.4310/jdg/1689262063

Cite this

@article{2f0931289d454276b56fa8e6df4528ba,

title = "HOMOGENIZATION OF RANDOM QUASICONFORMAL MAPPINGS AND RANDOM DELAUNEY TRIANGULATIONS",

abstract = "In this paper, we solve two problems dealing with the homogenization of random media. We show that a random quasiconformal mapping is close to an affine mapping, while a circle packing of a random Delauney triangulation is close to a conformal map, confirming a conjecture of K. Stephenson. We also show that on a Riemann surface equipped with a conformal metric, a random Delauney triangulation is close to being circle packed.",

author = "Oleg Ivrii and Vladimir Markovi{\'c}",

year = "2023",

month = jul,

doi = "https://doi.org/10.4310/jdg/1689262063",

language = "الإنجليزيّة",

volume = "124",

pages = "523--551",

journal = "Journal of Differential Geometry",

issn = "0022-040X",

publisher = "International Press of Boston, Inc.",

number = "3",

}

TY - JOUR

T1 - HOMOGENIZATION OF RANDOM QUASICONFORMAL MAPPINGS AND RANDOM DELAUNEY TRIANGULATIONS

AU - Ivrii, Oleg

AU - Marković, Vladimir

PY - 2023/7

Y1 - 2023/7

N2 - In this paper, we solve two problems dealing with the homogenization of random media. We show that a random quasiconformal mapping is close to an affine mapping, while a circle packing of a random Delauney triangulation is close to a conformal map, confirming a conjecture of K. Stephenson. We also show that on a Riemann surface equipped with a conformal metric, a random Delauney triangulation is close to being circle packed.

AB - In this paper, we solve two problems dealing with the homogenization of random media. We show that a random quasiconformal mapping is close to an affine mapping, while a circle packing of a random Delauney triangulation is close to a conformal map, confirming a conjecture of K. Stephenson. We also show that on a Riemann surface equipped with a conformal metric, a random Delauney triangulation is close to being circle packed.

UR - http://www.scopus.com/inward/record.url?scp=85165946063&partnerID=8YFLogxK

U2 - https://doi.org/10.4310/jdg/1689262063

DO - https://doi.org/10.4310/jdg/1689262063

M3 - مقالة

SN - 0022-040X

VL - 124

SP - 523

EP - 551

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

IS - 3

ER -

HOMOGENIZATION OF RANDOM QUASICONFORMAL MAPPINGS AND RANDOM DELAUNEY TRIANGULATIONS

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this