Stochastic tools on Hilbert manifolds: Interplay with geometry and physics

Communications in Mathematical Physics

Volumn 187, Issue 2, 1997, Pages 243-260

  Arnaudon, M ^a   Paycha, S ^b  

^a UNIVERSITÉ DE STRASBOURG   (France)

^b UNIVERSITÉ BLAISE PASCAL   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031476397     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050135     Document Type: Article

References (21)

1. Arnaudon, M., Paycha, S.: Factorization of semi-martingales on infinite dimensional principal bundles. Stochastics and Stochastic Reports, 53, 81-107 (1995)
2. Arnaudon, M., Paycha, S.: Regularisable and minimal orbits for group actions in infinite dimensions. Submitted to Commun. Math. Phys.
3. Belopolskaya, Ya. I., Daletskii, Yu. L.: Stochastic equations and Differential Geometry. Dorchrecht: Kluwer Academic Publishers, 1990
4. Asorey, M., Mitter, P. K.: Regularised, continuum Yang-Mills process and Feynman-Kac Functional integral, Commun. Math. Phys. 80, 43-58 (1981)
5. Abraham, R., Marsden, J. E., Ratiu, T.: Manifolds, tensor analysis and applications Global Analysis, Pure and Applied. In: Modern Methods for the study of non linear phenomena in engineering. Reading, MA: Addison Wesley, 1983
6. Gallot, S., Hulin, D., Lafontaine, J.: Riemannian geometry. Berlin-Heidelberg-New York: Springer Verlag, 1990 (second edition)
7. Daletskii, Yu.: Infinite-dimensional ellitpic operators and parabolic equations connected with them. Russ. Math. Surv. 22, 1-53 (1967)
8. Emery, M.: Stochastic calculus on manifolds. Berlin-Heidelberg-New York: Springer-Verlag, 1989
9. Paycha, S. Elliptic operators in the functional quantisation for gauge field theories. Commun. Math. Phys. 166, 433-455 (1995)
10. Tromba, A: Teichmüller Theory in Riemann Geometry. Boston-Basel-Berlin: Birkhäuser Verlag, 1992
11. Cheeger, J., Ebin, D. G.: Comparison Theorems in Riemannian Geometry. North Holland Mathematical Library, Amsterdam: North Holland Publishing Company, 1975
12. Chen, B. Y: Geometry of submanifolds. Pure and Applied Mathematics, A Series of monographs and textbooks, N.Y., 1973
13. Kuiper, N. H.: The homotopy type of the unitary group of Hilbert space. Topology 3, 19-30 (1965)
14. King, C.,Terng, C. L.: Volume and minimality of submanifolds in path space in "Global Analysis and Modern Mathematics", ed. K. Uhlenbeck, Publish or Perish (1994)
15. Elworthy, K. D.: Stochastic differential equations on manifolds. Lecture Note Series 70, Cambridge: Cambridge University Press, 1982
16. Eells, J., Lemaire, L.: Selected topics in harmonic maps. Conference Board for Mathematical Sciences, Regional Conference series 50, Providence, RI: A.M.S 1950
17. Gilkey, P .B.: Invariance Theory, The heat equation and the Atiyah-Singer index theorem, Wilmington, TE.Publish or Perish, 1984
18. Maeda, Y., Rosenberg, S., Tondeur, P.: The mean curvature of group orbits. In: "Global Analysis and Modern Mathematics", ed. K. Uhlenbeck, Publish or Perish, 1994
19. Narasimhan, M.S., Ramadas, T. R.: Geometry of SU(2) Gauge fields. Commun. Math. Phys. 67, 121-136 (1979)
20. Kondracki, W., Rogulski, J.: On the stratification of the orbit space. Dissertatione Mathematicae, Polish Acad. of Sci. 250, 1-62 (1986)
21. Ebin, D. G.: The manifold of Riemannian metrics. Proc. Symp. Pure Math. A.M.S.XV, 11-40 (1970)