The First Eigenvalue of the Laplacian and the Conductance of a Compact Surface
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We present some results whose central theme is the phenomenon of the first eigenvalue of the Laplacian and conductance of the dynamical system. Our main tool is a method for studying how the hyperbolic metric on a Riemann surface behaves under deformation of the surface. With this model, we show that there are variation of the first eigenvalue of the laplacian and the conductance of the dynamical system, with the Fenchel–Nielsen coordinates, that characterize the surface.
Key Wordsconductance Fenchel–Nielsen coordinates First eigenvalue of the Laplacian hyperbolic metric Riemann surface
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