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RESEARCH PRODUCT

Remarks on Martio’s conjecture

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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. peerReviewed