Conformal Wasserstein distances: comparing surfaces in polynomial time

Research output: Contribution to journalArticlepeer-review

47 Citations (Scopus)


We present a constructive approach to surface comparison realizable by a polynomial-time algorithm. We determine the "similarity" of two given surfaces by solving a mass-transportation problem between their conformal densities. This mass transportation problem differs from the standard case in that we require the solution to be invariant under global Möbius transformations. We present in detail the case where the surfaces to compare are disk-like; we also sketch how the approach can be generalized to other types of surfaces.
Original languageEnglish
Pages (from-to)1047-1077
JournalAdvances in Mathematics
Issue number3
Publication statusPublished - 2011


  • Numerical analysis
  • Differential geometry


Dive into the research topics of 'Conformal Wasserstein distances: comparing surfaces in polynomial time'. Together they form a unique fingerprint.

Cite this