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. Dubinin, V. N. Teichmüller's Modulsatz and the Variation of the Dirichlet Integral / V. N. Dubinin // Siberian Mathematical Journal. – 2024. – Vol. 65, No. 2. – P. 289-294. – DOI 10.1134/S0037446624020058.

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/

UR - https://elibrary.ru/item.asp?id=67308247

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 -