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We use the time real analyticity of Ricci flow proved by Kotschwar to extenda result in ~\cite{B}, namely, we prove that the Laplace spectra of negativelycurved compact surfaces having same genus $\gamma \geq 2$, same area and samecurvature bounds vary in a "controlled way", of which we give a quantitativeestimate (Theorem 1.1 below). We also observe how said real analyticity canlead to unexpected conclusions about spectral properties of generic metrics ona compact surface of genus $\gamma \geq 2$ (Proposition 1.5 below).

Variation of Laplace spectra of compact "nearly" hyperbolic surfaces