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 -