  This paper reports some novel and intriguing discoveries about the
localization and geometrization phenomenon in plasmon resonances and the
intrinsic geometric structures of Neumann-Poincar\'e eigenfunctions. It is
known that plasmon resonance generically occurs in the quasi-static regime
where the size of the plasmonic inclusion is sufficiently small compared to the
wavelength. In this paper, we show that the global smallness condition on the
plasmonic inclusion can be replaced by a local high-curvature condition, and
the plasmon resonance occurs locally near the high-curvature point of the
plasmonic inclusion. We provide partial theoretical explanation and link with
the geometric structures of the Neumann- Poincar\'e (NP) eigenfunctions. The
spectrum of the Neumann-Poincar\'e operator has received significant attentions
in the literature. We show for the first time some intrinsic geometric
structures of the Neumann-Poincar\'e eigenfunctions near high-curvature points.
