Mollifier Smoothing of tensor fields on differentiable manifolds and applications to Riemannian Geometry
| dc.creator | Fukuoka, Ryuichi | |
| dc.date | 2006-08-09 | |
| dc.date.accessioned | 2026-07-07T07:21:35Z | |
| dc.date.available | 2026-07-07T07:21:35Z | |
| dc.description | Let M be a differentiable manifold. We say that a tensor field g defined on M is non-regular if g is in some local Lp space or if g is continuous. In this work we define a mollifier smoothing g_t of g that has the following feature: If g is a Riemannian metric of class C2, then the Levi-Civita connection and the Riemannian curvature tensor of g_t converges to the Levi-Civita connection and to the Riemannian curvature tensor of g respectively as t converges to zero. Therefore this mollifier smoothing is a good starting point in order to generalize objects of the classical Riemannian geometry to non-regular Riemannian manifolds. Finally we give some applications of this mollifier smoothing. In particular, we generalize the concept of Lipschitz-Killing curvature measure for some non-regular Riemannian manifolds. | |
| dc.description | 43 pages | |
| dc.identifier | https://arxiv.org/abs/math/0608230 | |
| dc.identifier | http://arxiv.org/abs/math/0608230 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115351 | |
| dc.subject | Differential Geometry | |
| dc.subject | Metric Geometry | |
| dc.subject | 53B21 (Primary); 41A35, 53A45, 53B20 (Secondary) | |
| dc.title | Mollifier Smoothing of tensor fields on differentiable manifolds and applications to Riemannian Geometry | |
| dc.type | text |