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The Smolyanov Surface Measure on Trajectories in a Riemannian Manifold
| Content Provider | Semantic Scholar |
|---|---|
| Author | Sidorova, Nadezda A. |
| Copyright Year | 2004 |
| Abstract | It has been shown in Refs. 2–6 that two natural definitions of surface measures, on the space of continuous paths in a compact Riemannian manifold embedded into ℝn, introduced in the paper by Smolyanov1 are equivalent; this means that there exists a natural object — the surface measure, which we call the Smolyanov surface measure. Moreover, it has been shown2–6 that this surface measure is equivalent to the Wiener measure and the corresponding density has been found. But the known proof of the equivalence of the two definitions of the surface measure is rather nonexplicit; in fact the densities of the measures corresponding to the two different definitions were found independently and only a posteriori it was discovered that those densities coincided. Our aim is to give a direct proof of this fact. We introduce a more restrictive definition of the surface measure as the weak limit of a standard Brownian motion in ℝn conditioned to be in the tubular e-neighborhood of the manifold at times 0=t0 |
| Starting Page | 461 |
| Ending Page | 471 |
| Page Count | 11 |
| File Format | PDF HTM / HTML |
| DOI | 10.1142/S0219025704001712 |
| Volume Number | 07 |
| Alternate Webpage(s) | http://www.homepages.ucl.ac.uk/~ucahnsi/Papers/idaqp.pdf |
| Alternate Webpage(s) | https://doi.org/10.1142/S0219025704001712 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
