= Wolpert generic spectral rigidity theorem
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= Wolpert's theorem
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= Wolpert theorem
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For closed <hyperbolic surfaces> of genus $g\geq2$, there is a closed proper real-analytic exceptional subset of <Teichmüller space> such that a surface outside it is determined up to <isometry> by its unmarked <length spectrum>, equivalently its <Laplace-Beltrami operator> <spectrum>. The analytic part of the proof controls possible spectral matchings using finite determining length data; the geometric part recognizes persistent matchings as changes of marking, using the <collar lemma> and variations of <Fenchel–Nielsen coordinates>. Orientation reversal remains invisible to the spectrum.
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