Sign and area in nodal geometry of Laplace eigenfunctions
Sign and area in nodal geometry of Laplace eigenfunctions
The paper deals with asymptotic nodal geometry for the Laplace-Beltrami operator on closed surfaces. Given an eigenfunction f corresponding to a large eigenvalue, we study local asymmetry of the distribution of sign( f ) with respect to the surface area. It is measured as follows: take any disc centered at …