Minimal surfaces of Riemann type in three-dimensional product manifolds

75 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Associate and conjugate minimal immersions in MxR (2005, background): “It should be remarked that in [8] one can find other examples of complete minimal surfaces in H(2) × R with intrinsic curvature equal to −1.”
Harmonic maps and constant mean curvature surfaces in H 2 x R (2007, background): “big number of contributions in recent years [Ros, MeRo2, MeRo1, NeRo1, Hau , ADR, SaTo, SaE, MMP].”
Totally umbilic surfaces in homogeneous 3-manifolds (2006, background): “l surface of H2 ×R, embedded and invariant under parabolic isometries. Consequently, M is foliated by horocycles. This minimal surface was considered by B. Daniel [6], R. Sa Earp [8] and L. Hauswirth [12]. 17 4.3. Hyperbolic case. The umbilicity condition is θ′(s) = sinθ(s)tanhρ(s) Proceeding as in ”
An asymptotic theorem for minimal surfaces and existence results for minimal graphs in $H^2 \times R$ (2007, unknown): “Let H be the parabolic complete minimal surface (foliated by horocycles) whose asymptotic boundary is the vertical segment {−1}×[0, π] ⊂ ∂∞H 2 × R with (∂∞H(2) × {0}) ∪ (∂∞H(2) × {π}), see [6], [10] and [18].”
Half‐space theorem, embedded minimal annuli and minimal graphs in the Heisenberg group (2007, methodology): “This family is derived from the two-parameter family of minimal surfaces of H(2) × R constructed in [12].”