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We review a recent new approach to the study of critical points of Laplacian eigenfunctions.
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R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953, xv+561 pp
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K. Burdzy and Z.-Q. Chen, Weak convergence of reflecting Brownian motions
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R. Bañuelos and K. Burdzy, On the “hot spots” conjecture of J. Rauch
1999
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K. Burdzy and W. Werner, A counterexample to the “hot spots” conjecture
1999
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R. F. Bass and K. Burdzy, Fiber Brownian motion and the “hot spots” problem
2000
Cited alongside, same era.
D. Jerison and N. Nadirashvili, The “hot spots” conjecture for domains with two axes of symmetry
2000
Cited alongside, same era.
M. N. Pascu, Scaling coupling of reflecting Brownian motions and the hot spots problem
2002
Cited alongside, same era.
R. Atar and K. Burdzy, On Neumann eigenfunctions in lip domains
2004
Cited alongside, same era.
K. Burdzy, The hot spots problem in planar domains with one hole
2005
Cited alongside, same era.
N. Filonov, On an inequality between Dirichlet and Neumann eigenvalues for the Laplace operator
2005
Cited alongside, same era.
B. Siudeja, Hot spots conjecture for a class of acute triangles
2015
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D. Krejčiřík and M. Tušek, Location of hot spots in thin curved strips
2019
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C. Judge and S. Mondal, Euclidean triangles have no hot spots
2020
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S. Steinerberger, Hot Spots in Convex Domains are in the Tips (up to an Inradius)
2020
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A. Kleefeld, The hot spots conjecture can be false: Some numerical examples
2021
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C. Judge and S. Mondal, Erratum: Euclidean triangles have no hot spots
2022
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J. P. Kelliher, Eigenvalues of the Stokes operator versus the Dirichlet Laplacian in the plane
2010
Cited alongside, same era.
Cited in the paper.
J. Rohleder, A new approach to the hot spots conjecture
Cited in the paper.
S. Steinerberger, An upper bound on the Hot Spots constant
Cited in the paper.
C. Judge and S. Mondal, Critical points of Laplace eigenfunctions on polygons
2022
Later among the works it cites.