Minimal surfaces in $\mathbb{R}^3$ properly projecting into $\mathbb{R}^2$

Details Minimal surfaces in $\mathbb{R}^3$ properly projecting into $\mathbb{R}^2$ Minimal surfaces in $\mathbb{R}^3$ properly projecting into $\mathbb{R}^2$

2009-10-21

arxiv.org/abs/0910.4124v3

Mathematics

Differential Geometry

24 pages, 7 figures, to appear in Journal of Differential Geometry

Scientific paper

For all open Riemann surface M and real number $\theta \in (0,\pi/4),$ we construct a conformal minimal immersion $X=(X_1,X_2,X_3):M \to \mathbb{R}^3$ such that $X_3+\tan(\theta) |X_1|:M \to \mathbb{R}$ is positive and proper. Furthermore, $X$ can be chosen with arbitrarily prescribed flux map. Moreover, we produce properly immersed hyperbolic minimal surfaces with non empty boundary in $\mathbb{R}^3$ lying above a negative sublinear graph.

Affiliated with

Also associated with

No associations

Rating

Minimal surfaces in $\mathbb{R}^3$ properly projecting into $\mathbb{R}^2$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Minimal surfaces in $\mathbb{R}^3$ properly projecting into $\mathbb{R}^2$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Minimal surfaces in $\mathbb{R}^3$ properly projecting into $\mathbb{R}^2$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-144523