Resumen de Focal points and sup-norms of eigenfunctions II: the two-dimensional case

Christopher D. Sogge, Steve Zelditch

• We use a purely dynamical argument on circle maps to improve a result in our accompanying article, [5], on real analytic surfaces possessing eigenfunctions that achieve maximal sup norm bounds. The improved result is that there exists a ‘pole’ p so that all geodesics emanating from p are smoothly closed.