Isometric immersions into $\mathbb {S}^n\times \mathbb {R}$ and $\mathbb {H}^n\times \mathbb {R}$ and applications to minimal surfaces
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Publication:3648195
DOI10.1090/S0002-9947-09-04555-3zbMath1213.53075MaRDI QIDQ3648195
Publication date: 24 November 2009
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Other special differential geometries (53A40)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A Hopf differential for constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times\mathbb R\)
- Screw motion surfaces in \(\mathbb H^2 \times \mathbb R\) and \(\mathbb S^2\times \mathbb R\)
- Minimal surfaces of Riemann type in three-dimensional product manifolds
- Associate and conjugate minimal immersions in \(M \times R\)
- Minimal surfaces in \(M^2\times \mathbb{R}\)
- Minimal surfaces in \(\mathbb{H}^2\times\mathbb{R}\).
- Complete surfaces of constant mean curvature-1 in the hyperbolic 3-space
- The theory of minimal surfaces in \(M\times \mathbb R\)
- On isometric immersions of riemannian manifolds
- Isoperimetric domains in the Riemannian product of a circle with a simply connected space form and applications to free boundary problems
- On the geometry of constant mean curvature one surfaces in hyperbolic space
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