Duke Mathematical Journal

Fiber Brownian motion and the "hot spots" problem

Richard F. Bass and Krzysztof Burdzy

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Duke Math. J., Volume 105, Number 1 (2000), 25-58.

First available in Project Euclid: 13 August 2004

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35P05: General topics in linear spectral theory 60J45: Probabilistic potential theory [See also 31Cxx, 31D05] 60J60: Diffusion processes [See also 58J65]


Bass, Richard F.; Burdzy, Krzysztof. Fiber Brownian motion and the "hot spots" problem. Duke Math. J. 105 (2000), no. 1, 25--58. doi:10.1215/S0012-7094-00-10512-1. https://projecteuclid.org/euclid.dmj/1092403814

Export citation


  • C. Bandle, Isoperimetric Inequalities and Applications, Monogr. Stud. Math. 7, Pitman, Boston, 1980.
  • R. Bañuelos and K. Burdzy, On the ``hot spots'' conjecture of J. Rauch, J. Funct. Anal. 164 (1999), 1--33.
  • R. F. Bass, Probabilistic Techniques in Analysis, Probab. Appl., Springer, New York, 1995.
  • R. F. Bass and M. T. Barlow, The construction of Brownian motion on the Sierpinski carpet, Ann. I. H. Poincaré Probab. Statist. 25 (1989), 225--257.
  • R. F. Bass and P. Hsu, Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains, Ann. Probab. 19 (1991), 486--508.
  • K. Burdzy and W. Kendall, Efficient Markovian couplings: Examples and counterexamples, to appear in Ann. Appl. Probab.
  • K. Burdzy and W. Werner, A counterexample to the ``hot spots'' conjecture, Ann. of Math. (2) 149 (1999), 309--317.
  • I. Chavel, Eigenvalues in Riemannian Geometry, Pure Appl. Math. 115, Academic Press, Orlando, 1984.
  • K. Itô and H. P. McKean, Diffusion Processes and Their Sample Paths, Springer, Berlin, 1974.
  • D. Jerison and N. Nadirashvili, The ``hot spots'' conjecture for domains with two axes of symmetry, preprint, 1999.
  • B. Kawohl, Rearrangements and Convexity of Level Sets in PDE, Lecture Notes in Math. 1150, Springer, Berlin, 1985.