TITLE

# Complete bounded null curves immersed in $${\mathbb {C}^3}$$ and $${\rm {SL}(2,\mathbb {C})}$$

AUTHOR(S)
Martin, Francisco; Umehara, Masaaki; Yamada, Kotaro
PUB. DATE
September 2009
SOURCE
Calculus of Variations & Partial Differential Equations;Sep2009, Vol. 36 Issue 1, p119
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
We construct a simply connected complete bounded mean curvature one surface in the hyperbolic 3-space $${\mathcal {H}^3}$$. Such a surface in $${\mathcal {H}^3}$$ can be lifted as a complete bounded null curve in $${\rm {SL}(2,\mathbb {C})}$$. Using a transformation between null curves in $${\mathbb {C}^3}$$ and null curves in $${\rm {SL}(2,\mathbb {C})}$$, we are able to produce the first examples of complete bounded null curves in $${\mathbb {C}^3}$$. As an application, we can show the existence of a complete bounded minimal surface in $${\mathbb {R}^3}$$ whose conjugate minimal surface is also bounded. Moreover, we can show the existence of a complete bounded immersed complex submanifold in $${\mathbb {C}^2}$$.
ACCESSION #
40926426

## Related Articles

• Erratum to: Characterization of Generalized Gradient Young Measures Generated by Sequences in W and BV. Kristensen, Jan; Rindler, Filip // Archive for Rational Mechanics & Analysis;Feb2012, Vol. 203 Issue 2, p693

No abstract available.

• Generalized gradient approximation model exchange holes for range-separated hybrids. Henderson, Thomas M.; Janesko, Benjamin G.; Scuseria, Gustavo E. // Journal of Chemical Physics;5/21/2008, Vol. 128 Issue 19, p194105

We propose a general model for the spherically averaged exchange hole corresponding to a generalized gradient approximation (GGA) exchange functional. Parameters are reported for several common GGAs. Our model is based upon that of Ernzerhof and Perdew [J. Chem. Phys. 109, 3313 (1998)]. It...

• Inexact trust region PGC method for large sparse unconstrained optimization. Li, Junxiang; Yan, Limei; Li, Shudong; Huo, Jiazhen // Computational Optimization & Applications;Apr2012, Vol. 51 Issue 3, p981

We present an algorithm, partitioning group correction (PGC) algorithm based on trust region and conjugate gradient method, for large-scale sparse unconstrained optimization. In large sparse optimization, computing the whole Hessian matrix and solving the Newton-like equations at each iteration...

• A note on an SORâ€like method for augmented systems. Changjun Li; Zheng Li; Evans, David J.; Tie Zhang // IMA Journal of Numerical Analysis;Oct2003, Vol. 23 Issue 4, p581

Golub et al. (2001, BIT, 41, 71â€“85) gave a generalized successive overâ€relaxation method for the augmented systems. In this paper, the connection between the SORâ€like method and the preconditioned conjugate gradient (PCG) method for the augmented systems is investigated. It is...

• Determining quasidiabatic coupled electronic state Hamiltonians using derivative couplings: A normal equations based method. Papas, Brian N.; Schuurman, Michael S.; Yarkony, David R. // Journal of Chemical Physics;9/28/2008, Vol. 129 Issue 12, p124104

A self-consistent procedure for constructing a quasidiabatic Hamiltonian representing Nstate coupled electronic states in the vicinity of an arbitrary point in nuclear coordinate space is described. The matrix elements of the Hamiltonian are polynomials of arbitrary order. Employing a crude...

• Solvability problem for nondiagonal elliptic systems with a quadratic nonlinearity in the gradient (The two-dimensional case). Arkhipova, A. // Journal of Mathematical Sciences;May2005, Vol. 127 Issue 2, p1821

The existence of a weak solution of the Dirichlet problem for nondiagonal elliptic systems with quadratic nonlinearity is proved in the two-dimensional case. The solution is established to be smooth in the closure of a given domain, with the exception of at most finitely many points. The result...

• Heat Flow of Harmonic Maps Whose Gradients Belong to $$L^{n}_{x}L^{\infty}_{t}$$. Changyou Wang; Sverak, V. // Archive for Rational Mechanics & Analysis;May2008, Vol. 188 Issue 2, p351

For any compact n-dimensional Riemannian manifold ( M, g) without boundary, a compact Riemannian manifold $$N \subset {\mathbb{R}}^{k}$$ without boundary, and 0 < T â‰¦ +âˆž, we prove that for n â‰§ 4, if u : M Ã— (0, T] â†’ N is a weak solution to the heat flow of harmonic...

• The DY Conjugate Gradient Method with Armijo-type Line Searches. Shujun Lian; Changyu Wang // Journal of Systems Science & Information;Jun2004, Vol. 2 Issue 2, p279

Two Armijo-type line searches are proposed in this paper for nonlinear conjugate gradient methods. The two Armijo-type line searches are shown to guarantee the global convergence of the DY method for the unconstrained minimization of nonconvex differentiable functions. Further, if the function...

• Functional Identification of the Nonlinear Thermal-Conductivity Coefficient by Gradient Methods. I. Conjugate Operators. Borukhov, V.; Timoshpol'skii, V. // Journal of Engineering Physics & Thermophysics;Jul2005, Vol. 78 Issue 4, p695

Consideration is given to the gradient methods of solution of the inverse heat-conduction problem on determination of the nonlinear coefficient Î»(T) without its preliminary finite-dimensional approximation.

Share