Monotonicity of saddle maps


We prove an analog of Schoen–Yau univalentness theorem for saddle maps between discs.

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    This is where we are cheating: the inverse image \(p^{-1}(\gamma )\) might be as terrible as a pseudoarc, where the order of points has no sense.


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We want to thank the anonymous referee for keen comments. Funding was provided by DFG Grants (Grant Nos. STA 1511/1-1, SPP 2026) and Division of Mathematical Sciences (Grant No. 1309340).

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Correspondence to Anton Petrunin.

Additional information

Anton Petrunin was partially supported by NSF Grant DMS 1309340. Stephan Stadler was supported by DFG Grants STA 1511/1-1 and SPP 2026.

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Petrunin, A., Stadler, S. Monotonicity of saddle maps. Geom Dedicata 198, 181–188 (2019).

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  • Univalentness theorem
  • Saddle map
  • saddle surface

Mathematics Subject Classification (2000)

  • 53C45
  • 53C43
  • 53C23