Applications of quaternionic holomorphic geometry to minimal surfaces
From MaRDI portal
Publication:507067
DOI10.1515/coma-2016-0015zbMath1359.30054OpenAlexW2550894734MaRDI QIDQ507067
Katrin Leschke, Katsuhiro Moriya
Publication date: 3 February 2017
Published in: Complex Manifolds (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1515/coma-2016-0015
Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Functions of hypercomplex variables and generalized variables (30G35) Riemann surfaces (30F99)
Related Items (5)
Simple factor dressing and the López-Ros deformation of minimal surfaces in Euclidean 3-space ⋮ The \(\mu\)-Darboux transformation of minimal surfaces ⋮ Applications of quaternionic holomorphic geometry to minimal surfaces ⋮ Minimal surfaces in ${\mathbb{R}}^{4}$ foliated by conic sections and parabolic rotations of holomorphic null curves in ${\mathbb{C}}^{4}$ ⋮ Global solvability criteria for quaternionic Riccati equations
Cites Work
- Applications of quaternionic holomorphic geometry to minimal surfaces
- Harmonic tori in symmetric spaces and commuting Hamiltonian systems on loop algebras
- A duality theorem for Willmore surfaces
- On surfaces of stationary area bounded by two circles, or convex curves, in parallel planes
- All constant mean curvature tori in \(R^ 3\), \(S^ 3\), \(H^ 3\) in terms of theta-functions
- A complete embedded minimal surface in \({\mathbb{R}}^ 3\) with genus one and three ends
- The conformal Gauss map of submanifolds of the Möbius space
- Harmonic maps into Lie groups (classical solutions of the chiral model)
- Quaternionic analysis on Riemann surfaces and differential geometry
- On the connection between harmonic maps and the self-dual Yang-Mills and the sine-Gordon equations
- Weierstrass type representation of harmonic maps into symmetric spaces
- Curved flats and isothermic surfaces
- Quaternionic holomorphic geometry: Plücker formula, Dirac eigenvalue estimates and energy estimates of harmonic \(2\)-tori.
- Willmore immersions and loop groups
- On the classification of constant mean curvature tori
- Dressing orbits of harmonic maps
- Isothermic surfaces in \(\mathbf E^3\) as soliton surfaces
- Properly embedded minimal planar domains
- The Plateau problem for marginally outer trapped surfaces
- Harmonic maps from a 2-torus to the 3-sphere
- Global properties of minimal surfaces in \(E^ 3\) and \(E^ n\)
- Simple factor dressing and the López-Ros deformation of minimal surfaces in Euclidean 3-space
- On embedded complete minimal surfaces of genus zero
- Conformal maps from a 2-torus to the 4-sphere
- Euclidean Minimal Tori with Planar Ends and Elliptic Solitons
- Properly embedded minimal planar domains with infinite topology are Riemann minimal examples
- Willmore Surfaces with a Duality in S N (1)
- Bäcklund transformations and loop group actions
- Example of a complete minimal immersion in IR3 of genus one and three-embedded ends
- Conformal geometry of surfaces in \(S^4\) and quaternions
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Applications of quaternionic holomorphic geometry to minimal surfaces
