Duke Mathematical Journal

Fiber Brownian motion and the "hot spots" problem

Richard F. Bass and Krzysztof Burdzy

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Article information

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

Dates
First available in Project Euclid: 13 August 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1092403814

Mathematical Reviews number (MathSciNet)
MR1788041

Digital Object Identifier
doi:10.1215/S0012-7094-00-10512-1

Zentralblatt MATH identifier
1006.60078

Subjects
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]

Citation

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. http://projecteuclid.org/euclid.dmj/1092403814.


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References

  • 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.