##
Hot Spots Problem Illustrated

A painting by Ellsworth Kelly illustrates
the following open problem.

** Is it true that the second Neumann
eigenfunction in a triangle with acute angles
attains its maximum and minimum on the boundary
of the triangle? **
The green and red areas in the painting
are conjectured to represent parts
of the triangle where the second Neumann
eigenfunction is negative and postive.

Ellsworth Kelly *Two Panels: Green Orange*
(1970)

Oil on canvas,
Carnegie Musuem of Art, Pittsburgh
For more information on the "hot spots"
problem, see

- K. Burdzy and R. Bañuelos,
On the "hot spots" conjecture of J. Rauch
* J. Func. Anal.* **164** (1999) 1-33
- K. Burdzy and W. Werner,
A counterexample to the "hot spots" conjecture
*Ann. Math.* **149** (1999) 309-317
- R. Atar and K. Burdzy,
On Neumann eigenfunctions in lip domains
*Journal AMS * **17** (2004) 243-265
- K. Burdzy,
Neumann eigenfunctions and Brownian couplings
*
Potential theory in Matsue.
Proceedings of the International Workshop on Potential Theory,
Matsue 2004. Advanced Studies in
Pure Mathematics 44*. Mathematical Society of Japan, 2006,
pp. 11-23
(review paper)