Abstract
We construct the surface measure on the space C([0,1], M) of paths in a compact Riemannian manifold M without boundary embedded into R n which is induced by the usual flat Wiener measure on C([0,1], R n) conditioned to the event that the Brownian particle does not leave the tubular ε-neighborhood of M up to time 1. We prove that the limit as ε→0 exists, the limit measure is equivalent to the Wiener measure on C([0,1], M), and we compute the corresponding density explicitly in terms of scalar and mean curvature.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
