Remarks on Martio’s conjecture
Tengvall, V. (2022). Remarks on Martio’s conjecture. Mathematica Scandinavica, 128(3), 534-552. https://doi.org/10.7146/math.scand.a-132257
Published inMathematica Scandinavica
© Aarhus Universitet, 2022
We introduce a certain integrability condition for the reciprocal of the Jacobian determinant whichguarantees the local homeomorphism property of quasiregular mappings with a small inner dilata-tion. This condition turns out to be sharp in the planar case. We also show that every branch pointof a quasiregular mapping with a small inner dilatation is a Lebesgue point of the differentialmatrix of the mapping.
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Additional information about fundingThis work was supported by the Academy of Finland, project number 308759.
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