arXiv subjects

Paul A. Schweitzer S. J

Publications and source records attributed to Paul A. Schweitzer S. J.

2 recordsLinked to original sources

arXiv2022

Asymptotic linking of volume-preserving actions of ${\mathbb R}^k$

We extend V. Arnold's theory of asymptotic linking for two volume preserving flows on a domain in ${\mathbb R}^3$ and $S^3$ to volume preserving actions of ${\mathbb R}^k$ and ${\mathbb R}^\ell$ on certain domains in ${\mathbb R}^n$ and also to linking of a volume preserving action of ${\mathbb R}^k$ with a closed oriented singular $\ell$-dimensional submanifold in ${\mathbb R}^n$, where $n=k+\ell+1$. We also extend the Biot-Savart formula to higher dimensions.

math.DG↗

arXiv2012

Locally convex hypersurfaces immersed in $H^n \times R$

We prove a theorem of Hadamard-Stoker type: a connected locally convex complete hypersurface immersed in $H^n \times R$ (n>1), where $H^n$ is n-dimensional hyperbolic space, is embedded and homeomorphic either to the n-sphere or to $R^n$. In the latter case it is either a vertical graph over a convex domain in $H^n$ or has what we call a simple end.

math.DG↗