Marked length spectra and areas of non-positively curved cone metrics
The paper is devoted to the two types of metrics on a closed surface \(X\): a negatively curved cone metric and a flat cone metric. The author obtained two main results for these metrics. The first result relates to the space of isotopy classes of negatively curved cone metrics. The theorem proved in the paper states that an inequality between their marked length spectra implies a similar inequality between their areas. The second result is similar to the first one and relates to the space of isotopy classes of flat cone metrics. The proof of the theorem expressing the result is also similar to the previous one.
scientific article; zbMATH DE number 6493235