Skip to Main content Skip to Navigation
Theses

Constant mean curvature surfaces in euclidean and hyperbolic spaces

Abstract : Non-zero constant mean curvature surfaces are mathematical models for physical interface problems with non-zero pressure difference. They are described by partial differential equations and can be constructed from holomorphic data via a Weierstrass-type representation, called "the DPW method". In this thesis, we use the DPW method and prove two main results. The frst one states that perturbations of the DPW data for Delaunay unduloidal ends generate embedded annuli. This can be used to prove the embeddedness of surfaces constructed via the DPW method. The second result is the construction of n-noids in Hyperbolic space: genus 0, embedded, constant mean curvature surfaces with n Delaunay ends.
Complete list of metadatas

Cited literature [44 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-02410140
Contributor : Thomas Raujouan <>
Submitted on : Friday, December 13, 2019 - 4:56:01 PM
Last modification on : Wednesday, December 18, 2019 - 1:41:05 AM

File

These.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : tel-02410140, version 1

Collections

Citation

Thomas Raujouan. Constant mean curvature surfaces in euclidean and hyperbolic spaces. Mathematics [math]. Université de Tours, 2019. English. ⟨tel-02410140⟩

Share

Metrics

Record views

46

Files downloads

64