Integrals on a moving manifold and geometrical probability
- 1 March 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 9 (03) , 588-603
- https://doi.org/10.1017/s0001867800028998
Abstract
For a manifold which is moving and changing with time, consider some numerical property which at each instant is equal to an integral over the manifold. We derive a general expression for the time rate of change of this integral. Corollaries include a precise general form of Crofton's boundary theorem, de Hoff's interface displacement equations (with some new extensions) and a theorem in fluid mechanics.Keywords
This publication has 1 reference indexed in Scilit:
- A more general form of a theorem of CroftonJournal of Applied Probability, 1973