# Unique Determination of 3-Connected Plane Domains by Relative Conformal Moduli of Pairs of Boundary Components

## Abstract

We study the boundary values of conformal mappings of plane finitely connected domains. We present a complete exposition of a theorem giving an exhaustive description of the boundary values of such mappings in terms of conformal moduli (extremal lengths) of pairs of boundary components of a domain of connectedness at most 3. Bibliography: 12 titles.

- Authors:

- Sobolev Institute of Mathematics SB RAS (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771211

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 231; Journal Issue: 2; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; BOUNDARY-VALUE PROBLEMS; CONFORMAL INVARIANCE; CONFORMAL MAPPING; EQUATIONS; FINITE ELEMENT METHOD

### Citation Formats

```
Kopylov, A. P., E-mail: apkopylov@yahoo.com.
```*Unique Determination of 3-Connected Plane Domains by Relative Conformal Moduli of Pairs of Boundary Components*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3814-0.

```
Kopylov, A. P., E-mail: apkopylov@yahoo.com.
```*Unique Determination of 3-Connected Plane Domains by Relative Conformal Moduli of Pairs of Boundary Components*. United States. doi:10.1007/S10958-018-3814-0.

```
Kopylov, A. P., E-mail: apkopylov@yahoo.com. Tue .
"Unique Determination of 3-Connected Plane Domains by Relative Conformal Moduli of Pairs of Boundary Components". United States. doi:10.1007/S10958-018-3814-0.
```

```
@article{osti_22771211,
```

title = {Unique Determination of 3-Connected Plane Domains by Relative Conformal Moduli of Pairs of Boundary Components},

author = {Kopylov, A. P., E-mail: apkopylov@yahoo.com},

abstractNote = {We study the boundary values of conformal mappings of plane finitely connected domains. We present a complete exposition of a theorem giving an exhaustive description of the boundary values of such mappings in terms of conformal moduli (extremal lengths) of pairs of boundary components of a domain of connectedness at most 3. Bibliography: 12 titles.},

doi = {10.1007/S10958-018-3814-0},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 2,

volume = 231,

place = {United States},

year = {2018},

month = {5}

}

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