Evolution of networks with multiple junctions / Carlo Mantegazza, Matteo Novaga, Alessandra Pluda & Felix Schulze.

Format:

Book

Author/Creator:

Mantegazza, Carlo, author.

Novaga, Matteo, author.

Pluda, Alessandra, author.

Schulze, Felix, author.

Contributor:

Société mathématique de France.

Series:

Astérisque ; 452.

Astérisque, 0303-1179 ; 452

Language:

English

Subjects (All):

Geometry, Differential.

Function spaces.

Curves.

Physical Description:

viii, 254 pages : illustrations ; 24 cm.

Place of Publication:

Paris : Société Mathématique de France, 2024.

Summary:

"We consider the motion by curvature of a network of curves in the plane and we discuss existence, uniqueness, singularity formation, and asymptotic behavior of the flow." -- Back cover.

Contents:

1. Introduction

2. Notation, definitions, and basic computations

3. Short time existence I

4. Integral estimates

5. Short-time existence II

6. Smooth flows Brakke flows

7. The monotonicity formula and the rescaling procedures

8. Classification of possible blow-up limits

9. Local regularity

10. The behavior of the flow at a singular time

11. Short time existence III - Non-regular networks

12. Restarting the flow after a singular time

13. Long time behavior

14. An isoperimetric estimate

15. The flow of networks with at most two triple junctions

16. Open problems.

Notes:

Includes bibliographical references (page 247-254).

ISBN:

9782856299975

2856299970

OCLC:

1468607722