# Interfacial Dynamics of Abelian Domains: Differential Geometric Methods

## Abstract

The equation: ReF`(T,Z)ZF`(T,Z) = 1 for conformal maps f(t,z) is important in interfacial dynamics. We extend the results by Gustafsson on existence and uniqueness of solutions of this equation from the case when f(t,z) is a rational function of z to the case when the spatial derivative f`(t,z) is rational.

- Authors:

- Publication Date:

- Research Org.:
- Los Alamos National Lab., NM (United States). Applied Theoretical Physics Div.

- Sponsoring Org.:
- USDOE Assistant Secretary for Human Resources and Administration, Washington, DC (United States)

- OSTI Identifier:
- 626473

- Report Number(s):
- LA-UR-97-4250; CONF-971167-

ON: DE98002659; TRN: 98:006923

- DOE Contract Number:
- W-7405-ENG-36

- Resource Type:
- Conference

- Resource Relation:
- Conference: NOLTA `97: international symposium on nonlinear theory and its applications, Honolulu, HI (United States), 29 Nov - 3 Dec 1997; Other Information: PBD: [Nov 1997]

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING NOT INCLUDED IN OTHER CATEGORIES; 66 PHYSICS; MATHEMATICS; VISCOUS FLOW; MAPPING; TRANSFORMATIONS; INCOMPRESSIBLE FLOW; CAUCHY PROBLEM; PARTIAL DIFFERENTIAL EQUATIONS

### Citation Formats

```
Owczarek, Robert M, and Makaruk, Hanna E.
```*Interfacial Dynamics of Abelian Domains: Differential Geometric Methods*. United States: N. p., 1997.
Web.

```
Owczarek, Robert M, & Makaruk, Hanna E.
```*Interfacial Dynamics of Abelian Domains: Differential Geometric Methods*. United States.

```
Owczarek, Robert M, and Makaruk, Hanna E. Wed .
"Interfacial Dynamics of Abelian Domains: Differential Geometric Methods". United States. https://www.osti.gov/servlets/purl/626473.
```

```
@article{osti_626473,
```

title = {Interfacial Dynamics of Abelian Domains: Differential Geometric Methods},

author = {Owczarek, Robert M and Makaruk, Hanna E},

abstractNote = {The equation: ReF`(T,Z)ZF`(T,Z) = 1 for conformal maps f(t,z) is important in interfacial dynamics. We extend the results by Gustafsson on existence and uniqueness of solutions of this equation from the case when f(t,z) is a rational function of z to the case when the spatial derivative f`(t,z) is rational.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1997},

month = {12}

}

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