Burdzy, KrzysztofBass, Richard F.2005-11-292005-11-292000-10Bass, R.F. & K. Burdzy. (2000). Fiber Brownian motion and the "hot spots" problem. Duke Mathematical Journal, 105(1), 25-58.http://hdl.handle.net/1773/2203We show that in some planar domains both extrema of the second Neumann eigenfunction lie strictly inside the domain. The main technical innovation is the use of "fiber Brownian motion," a process which switches between two-dimensional and one-dimensional evolution.272426 bytesapplication/pdfen-USPlanar Brownian motionNeumann eigenfunctionsfiber Brownian motionArticle