# Rigidity of piecewise convex surfaces of torus type

## Abstract

Closed genus-one surfaces pasted from finitely many pieces of convex C{sup 2}-surfaces are considered. Vertices and conical points are allowed. An algorithm for the construction of such surfaces is given. They are proved to be rigid outside at domains with respect to infinitesimal bendings of the first order with continuous bending fields belonging to the class C{sup 2} on each C{sup 2}-smooth piece.

- Authors:

- Rostov State University, Rostov-on-Don (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 21202917

- Resource Type:
- Journal Article

- Journal Name:
- Sbornik. Mathematics

- Additional Journal Information:
- Journal Volume: 191; Journal Issue: 4; Other Information: DOI: 10.1070/SM2000v191n04ABEH000473; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; CONVEX MANIFOLDS; SMOOTH MANIFOLDS; SURFACES; TORI

### Citation Formats

```
Markov, P E, and Shkryl', E V.
```*Rigidity of piecewise convex surfaces of torus type*. United States: N. p., 2000.
Web. doi:10.1070/SM2000V191N04ABEH000473; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).

```
Markov, P E, & Shkryl', E V.
```*Rigidity of piecewise convex surfaces of torus type*. United States. doi:10.1070/SM2000V191N04ABEH000473; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).

```
Markov, P E, and Shkryl', E V. Sun .
"Rigidity of piecewise convex surfaces of torus type". United States. doi:10.1070/SM2000V191N04ABEH000473; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
```

```
@article{osti_21202917,
```

title = {Rigidity of piecewise convex surfaces of torus type},

author = {Markov, P E and Shkryl', E V},

abstractNote = {Closed genus-one surfaces pasted from finitely many pieces of convex C{sup 2}-surfaces are considered. Vertices and conical points are allowed. An algorithm for the construction of such surfaces is given. They are proved to be rigid outside at domains with respect to infinitesimal bendings of the first order with continuous bending fields belonging to the class C{sup 2} on each C{sup 2}-smooth piece.},

doi = {10.1070/SM2000V191N04ABEH000473; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},

journal = {Sbornik. Mathematics},

issn = {1064-5616},

number = 4,

volume = 191,

place = {United States},

year = {2000},

month = {4}

}

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