Standard

Teichmüller’s Modulsatz and the Variation of the Dirichlet Integral. / Dubinin, V. N.

In: Siberian Mathematical Journal, Vol. 65, No. 2, 03.2024, p. 289-294.

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

Harvard

Dubinin, VN 2024, 'Teichmüller’s Modulsatz and the Variation of the Dirichlet Integral', Siberian Mathematical Journal, vol. 65, no. 2, pp. 289-294. https://doi.org/10.1134/S0037446624020058

APA

Dubinin, V. N. (2024). Teichmüller’s Modulsatz and the Variation of the Dirichlet Integral. Siberian Mathematical Journal, 65(2), 289-294. https://doi.org/10.1134/S0037446624020058

Vancouver

Dubinin VN. Teichmüller’s Modulsatz and the Variation of the Dirichlet Integral. Siberian Mathematical Journal. 2024 Mar;65(2):289-294. doi: 10.1134/S0037446624020058

Author

Dubinin, V. N. / Teichmüller’s Modulsatz and the Variation of the Dirichlet Integral. In: Siberian Mathematical Journal. 2024 ; Vol. 65, No. 2. pp. 289-294.

BibTeX

@article{776f5523355447d0857ac729ab48c6aa,
title = "Teichm{\"u}ller{\textquoteright}s Modulsatz and the Variation of the Dirichlet Integral",
abstract = "We show thatchanging the level curve of a harmonic functionwith the classical Hadamard variation with a small parameterentails a change in the Dirichlet integral of the functionwhich is quadratic in the parameter.As a corollary,we supplement the well-known theorem of Teichm{\"u}llerabout the sum of moduli of doubly connected domainsinto which an annulus is subdividedby a continuum that differs little from a concentric circle.",
keywords = "517.956.224, Dirichlet integral, condenser capacity, harmonic function, modulus of a doubly connected domain",
author = "Dubinin, {V. N.}",
note = "The work was supported by the Mathematical Center in Akademgorodok under the agreement no. 075–15–2022–282 with the Ministry of Science and Higher Education of the Russian Federation. ",
year = "2024",
month = mar,
doi = "10.1134/S0037446624020058",
language = "English",
volume = "65",
pages = "289--294",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",
number = "2",

}

RIS

TY - JOUR

T1 - Teichmüller’s Modulsatz and the Variation of the Dirichlet Integral

AU - Dubinin, V. N.

N1 - The work was supported by the Mathematical Center in Akademgorodok under the agreement no. 075–15–2022–282 with the Ministry of Science and Higher Education of the Russian Federation.

PY - 2024/3

Y1 - 2024/3

N2 - We show thatchanging the level curve of a harmonic functionwith the classical Hadamard variation with a small parameterentails a change in the Dirichlet integral of the functionwhich is quadratic in the parameter.As a corollary,we supplement the well-known theorem of Teichmüllerabout the sum of moduli of doubly connected domainsinto which an annulus is subdividedby a continuum that differs little from a concentric circle.

AB - We show thatchanging the level curve of a harmonic functionwith the classical Hadamard variation with a small parameterentails a change in the Dirichlet integral of the functionwhich is quadratic in the parameter.As a corollary,we supplement the well-known theorem of Teichmüllerabout the sum of moduli of doubly connected domainsinto which an annulus is subdividedby a continuum that differs little from a concentric circle.

KW - 517.956.224

KW - Dirichlet integral

KW - condenser capacity

KW - harmonic function

KW - modulus of a doubly connected domain

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85188647101&origin=inward&txGid=53d968cce96291d1b74687f367c1e566

UR - https://www.mendeley.com/catalogue/b96b2af7-8b7e-3f7b-8d18-f6fed48b07b0/

U2 - 10.1134/S0037446624020058

DO - 10.1134/S0037446624020058

M3 - Article

VL - 65

SP - 289

EP - 294

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 2

ER -

ID: 61124745