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Submanifolds of Constant Negative Curvature: A Generalization of Hilbert's Theorem
John Douglas Moore
We use the generalized Gauss-Bonnet formula for Riemannian polyhedra discovered by Allendoerfer, Weil and Chern to show that hyperbolic space of dimension has no isometric imme…
Self-intersections of Closed Parametrized Minimal Surfaces in Generic Riemannian Manifolds
John Douglas Moore
This article shows that for generic choice of Riemannian metric on a smooth manifold of dimension four, all prime compact parametrized minimal surfaces within have self-int…
Closed minimal surfaces of high Morse index in manifolds of negative curvature
John Douglas Moore
We show that compact Riemannian three-manifolds with negative sectional curvature possess closed minimal surfaces of arbitrarily high Morse index.
Minimal two-spheres of low index in manifolds of positive complex sectional curvature
John Douglas Moore, Robert Ream
Suppose that is given a generic Riemannian metric with sectional curvatures which satisfy a suitable pinching condition formulated in terms of complex sectional curvatures. T…
Bumpy Riemannian metrics and closed parametrized minimal surfaces in Riemannian manifolds
John Douglas Moore
This article proves that if M is a smooth manifold of dimension at least four, then for generic choice of metric on M, all prime parametrized minimal surfaces in M are free of bran…