Marked length spectra and areas of non-positively curved cone metrics
type: Item
instance of: scholarly article
title: Marked length spectra and areas of non-positively curved cone metrics
zbMATH Open document ID: 1365.51010
published in: Geometriae Dedicata
publication date: 2015-10-12T00:00:00Z
review text: 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.
reviewed by: Victor Oxman
Mathematics Subject Classification ID: 51M25
Mathematics Subject Classification ID: 53C24
zbMATH DE Number: 6493235
zbMATH Keywords: area
zbMATH Keywords: flat cone metric
zbMATH Keywords: holomorphic quadratic differential
zbMATH Keywords: marked length spectrum
zbMATH Keywords: negatively curved cone metric
author: Zongliang Sun
MaRDI profile type: Publication
full work available at URL: s10711-015-0052-1
OpenAlex ID: W1969263853
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DOI: 10.1007/S10711-015-0052-1
description: scientific article; zbMATH DE number 6493235