2 citations · 2 across the 6 of their papers we have counts for
4 papers · 1 filter
Hot spots on cones and warped product manifolds
Lawford Hatcher
We study extrema of solutions to the heat equation (i.e. hot spots) on a class of warped product manifolds of the form where is a closed Riem…
A hot spots theorem for the mixed eigenvalue problem with small Dirichlet region
Lawford Hatcher
We prove that on convex domains, first mixed Laplace eigenfunctions have no interior critical points if the Dirichlet region is connected and sufficiently small. We also find two s…
The hot spots conjecture for some non-convex polygons
Lawford Hatcher
We give an elementary new proof of the hot spots conjecture for L-shaped domains. This result, in addition to a new eigenvalue inequality, allows us to locate the hot spots in Swis…
First mixed Laplace eigenfunctions with no hot spots
Lawford Hatcher
The hot spots conjecture of J. Rauch states that the second Neumann eigenfunction of the Laplace operator on a bounded Lipschitz domain in attains its extrema only o…