Mappings of finite distortion: Size of the branch set

References

[1] M. Aaltonen, Monodromy representations of completed coverings, Rev. Mat. Iberoam. 32 (2016), no. 2, 533–570. 10.4171/RMI/894Search in Google Scholar

[2] M. Aaltonen and P. Pankka, Local monodromy of branched covers and dimension of the branch set, Ann. Acad. Sci. Fenn. Math. 42 (2017), no. 1, 487–496. 10.5186/aasfm.2017.4231Search in Google Scholar

[3] L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Math. Monogr., Oxford University Press, New York, 2000. Search in Google Scholar

[4] K. Astala, T. Iwaniec and G. Martin, Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane, Princeton Math. Ser. 48, Princeton University Press, Princeton, 2009. 10.1515/9781400830114Search in Google Scholar

[5] J. M. Ball, Global invertibility of Sobolev functions and the interpenetration of matter, Proc. Roy. Soc. Edinburgh Sect. A 88 (1981), no. 3–4, 315–328. 10.1017/S030821050002014XSearch in Google Scholar

[6] C. J. Bishop, Quasiconformal mappings which increase dimension, Ann. Acad. Sci. Fenn. Math. 24 (1999), no. 2, 397–407. Search in Google Scholar

[7] A. V. Černavskiĭ, Finite-to-one open mappings of manifolds, Mat. Sb. (N.S.) 65(107) (1964), 357–369. 10.1090/trans2/100/10Search in Google Scholar

[8] A. V. Černavskiĭ, Addendum to the paper “Finite-to-one open mappings of manifolds”, Mat. Sb. (N.S.) 66(108) (1965), 471–472. Search in Google Scholar

[9] M. Csörnyei, S. Hencl and J. Malý, Homeomorphisms in the Sobolev space W1,n-1, J. Reine Angew. Math. 644 (2010), 221–235. Search in Google Scholar

[10] F. W. Gehring and J. Väisälä, Hausdorff dimension and quasiconformal mappings, J. Lond. Math. Soc. (2) 6 (1973), 504–512. 10.1112/jlms/s2-6.3.504Search in Google Scholar

[11] C.-Y. Guo, Mappings of finite inner distortion: Global homeomorphism theorem, J. Geom. Anal. 25 (2015), no. 3, 1969–1991. 10.1007/s12220-014-9500-7Search in Google Scholar

[12] J. Heinonen and P. Koskela, Sobolev mappings with integrable dilatations, Arch. Ration. Mech. Anal. 125 (1993), no. 1, 81–97. 10.1007/BF00411478Search in Google Scholar

[13] J. Heinonen and S. Rickman, Quasiregular maps 𝐒3→𝐒3 with wild branch sets, Topology 37 (1998), no. 1, 1–24. 10.1016/S0040-9383(97)00015-3Search in Google Scholar

[14] J. Heinonen and S. Rickman, Geometric branched covers between generalized manifolds, Duke Math. J. 113 (2002), no. 3, 465–529. 10.1215/S0012-7094-02-11333-7Search in Google Scholar

[15] S. Hencl and P. Koskela, Lectures on Mappings of Finite Distortion, Lecture Notes in Math. 2096, Springer, Cham, 2014. 10.1007/978-3-319-03173-6Search in Google Scholar

[16] S. Hencl and K. Rajala, Optimal assumptions for discreteness, Arch. Ration. Mech. Anal. 207 (2013), no. 3, 775–783. 10.1007/s00205-012-0574-8Search in Google Scholar

[17] S. Hencl and V. Tengvall, Sharpness of the differentiability almost everywhere and capacitary estimates for Sobolev mappings, Rev. Mat. Iberoam. 33 (2017), no. 2, 595–622. 10.4171/RMI/951Search in Google Scholar

[18] T. Iwaniec, P. Koskela and J. Onninen, Mappings of finite distortion: Monotonicity and continuity, Invent. Math. 144 (2001), no. 3, 507–531. 10.1007/s002220100130Search in Google Scholar

[19] T. Iwaniec and G. Martin, Geometric Function Theory and Nonlinear Analysis, Oxford Math. Monogr., Oxford University Press, New York, 2001. Search in Google Scholar

[20] T. Iwaniec and G. Martin, The Beltrami equation, Mem. Amer. Math. Soc. 191 (2008), no. 893, 1–92. 10.1090/memo/0893Search in Google Scholar

[21] T. Iwaniec and V. Šverák, On mappings with integrable dilatation, Proc. Amer. Math. Soc. 118 (1993), no. 1, 181–188. 10.1090/S0002-9939-1993-1160301-5Search in Google Scholar

[22] J. Kauhanen, P. Koskela and J. Malý, Mappings of finite distortion: Condition N, Michigan Math. J. 49 (2001), no. 1, 169–181. 10.1307/mmj/1008719040Search in Google Scholar

[23] J. Kauhanen, P. Koskela and J. Malý, Mappings of finite distortion: discreteness and openness, Arch. Ration. Mech. Anal. 160 (2001), no. 2, 135–151. 10.1007/s002050100162Search in Google Scholar

[24] J. Kauhanen, P. Koskela, J. Malý, J. Onninen and X. Zhong, Mappings of finite distortion: Sharp Orlicz-conditions, Rev. Mat. Iberoam. 19 (2003), no. 3, 857–872. 10.4171/RMI/372Search in Google Scholar

[25] P. Koskela and J. Malý, Mappings of finite distortion: the zero set of the Jacobian, J. Eur. Math. Soc. (JEMS) 5 (2003), no. 2, 95–105. 10.1007/s10097-002-0046-9Search in Google Scholar

[26] P. Koskela and J. Onninen, Mappings of finite distortion: Capacity and modulus inequalities, J. Reine Angew. Math. 599 (2006), 1–26. 10.1515/CRELLE.2006.076Search in Google Scholar

[27] O. Martio, A capacity inequality for quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I (1970), no. 474, 1–18. 10.5186/aasfm.1971.474Search in Google Scholar

[28] O. Martio, S. Rickman and J. Väisälä, Definitions for quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I 448 (1969), 1–40. 10.5186/aasfm.1969.448Search in Google Scholar

[29] J. Onninen, Differentiability of monotone Sobolev functions, Real Anal. Exchange 26 (2000/01), no. 2, 761–772. 10.2307/44154076Search in Google Scholar

[30] E. A. Poletskiǐ, The modulus method for non-homeomorphic quasiregular mappings (in Russian), Mat. Sb. 83 (1970), 261–273. Search in Google Scholar

[31] Y. G. Reshetnyak, Space Mappings with Bounded Distortion, Transl. Math. Monogr. 73, American Mathematical Society, Providence, 1989. 10.1090/mmono/073Search in Google Scholar

[32] S. Rickman, Quasiregular Mappings, Ergeb. Math. Grenzgeb. (3) 26, Springer, Berlin, 1993. 10.1007/978-3-642-78201-5Search in Google Scholar

[33] V. Šverák, Regularity properties of deformations with finite energy, Arch. Ration. Mech. Anal. 100 (1988), no. 2, 105–127. 10.1007/BF00282200Search in Google Scholar

[34] V. Tengvall, Differentiability in the Sobolev space W1,n-1, Calc. Var. Partial Differential Equations 51 (2014), no. 1–2, 381–399. 10.1007/s00526-013-0679-4Search in Google Scholar

[35] J. Väisälä, Two new characterizations for quasiconformality, Ann. Acad. Sci. Fenn. Ser. A I 362 (1965), 1–12. Search in Google Scholar

[36] J. Väisälä, Discrete open mappings on manifolds, Ann. Acad. Sci. Fenn. Ser. A I 392 (1966), 1–10. 10.5186/aasfm.1967.392Search in Google Scholar

[37] J. Väisälä, Modulus and capacity inequalities for quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I (1972), no. 509, 1–14. 10.5186/aasfm.1972.509Search in Google Scholar