Riikka Korte

• Associate professor

• Address:
  Aalto University,
  Department of Mathematics and Systems Analysis,
  P.O. Box 11100,
  00076 Aalto, Finland

• Visiting Address:
  Otakaari 1, Espoo
  Room M225

• E-mail: firstname.lastname@aalto.fi
• Phone: +358 50 453 2909

Please come and discuss any time I'm in my office M225 or send me an email to make an appointment.

Research papers

(A link to my papers in MathSciNet)

Keep in mind that some of the downloads of the following papers are earlier versions of the final articles and therefore may differ from the journal article.

1. Geometric implications of the Poincaré inequality, Results Math., 50 (2007), no. 1-2, 93-107. Preprint.
2. Lebesgue points and capacities via the boxing inequality in metric spaces, (with Juha Kinnunen, Nageswari Shanmugalingam and Heli Tuominen), Indiana Univ. Math. J., 57(1), 401-430, 2008. Preprint.
3. Characterizations of Sobolev inequalities on metric spaces, (with Juha Kinnunen). J. Math. Anal. Appl., 344(2), 1093-1103, 2008. Preprint in arXiv.
4. A Caccioppoli estimate and fine continuity for superminimizers on metric spaces. Ann. Acad. Sci. Fenn. Math. 33 (2008), 597--604.
5. Obstacle problem for nonlinear parabolic equations, (with Tuomo Kuusi and Juhana Siljander). J. Differential Equations 246 (9), 3668-3680, 2009.
6. Characterizations for Hardy's inequality, (with Juha Kinnunen). Around the Research of Vladimir Maz'ya I, International Mathematical Series, Vol. 11, Laptev Ari (Ed.), 239-254, Springer, 2010.
7. Equivalence and self-improvement of p-fatness and Hardy's inequality, and association with uniform perfectness, (with Nageswari Shanmugalingam). Math. Z. 246(1), 99-110, 2010. Preprint in arXiv.
8. A note on the Wolff potential estimate for solutions to elliptic equations involving measures, (with Tuomo Kuusi). Adv. Calc. Var. March 2010. Vol. 3 No. 1:99-113. Preprint.
9. A connection between a general class of superparabolic functions and supersolutions, (with Tuomo Kuusi and Mikko Parviainen). J. Evol. Equ. 10(1), 1-20, 2010. Preprint.
10. The De Giorgi measure and an obstacle problem related to minimal surfaces in metric spaces, (with Juha Kinnunen, Nageswari Shanmugalingam and Heli Tuominen). J. Math. Pures Appl. 93 (2010), 599-622.
11. Stability of solutions of the double obstacle problem on metric spaces, (with Michela Eleuteri, Zohra Farnana and Outi Elina Kansanen), J. Anal. 18 (2010), 145-160. (Proceedings of the ICM2010 Satellite Conference International workshop on Harmonic and Quasiconformal Mappings (HQM2010)).
12. Strong A_∞-weights are A_∞-weights on metric spaces, (with Outi Elina Kansanen). Revista Mat. Iberoamericana 27(1), 335-354, 2011. Preprint in arXiv.
13. The equivalence between pointwise Hardy inequalities and uniform fatness, (with Juha Lehrbäck and Heli Tuominen). Math. Ann. 351 (2011), no. 3, 711--731. Preprint in arXiv.
14. A characterization of Newtonian functions with zero boundary values, (with Juha Kinnunen, Nageswari Shanmugalingam and Heli Tuominen). Calc. Var. PDE. 43 (2012), no. 3, 507--528. Preprint.
15. Quasiconformality, homeomorphisms between metric measure spaces preserving quasiminimizers, and uniform density property, (with Niko Marola and Nageswari Shanmugalingam). Ark. Mat., 50 (2012), 111-134. Preprint in CVGMT Pisa.
16. Measure of curves in graded groups, (with Valentino Magnani). Illinois J. Math. 56 (2012), no. 2, 353-366. Preprint in CVGMT Pisa.
17. Nonlinear parabolic capacity and polar sets of superparabolic functions, (with Juha Kinnunen, Tuomo Kuusi and Mikko Parviainen). Math. Ann. 355 (2013), no. 4, 1349-1381. Preprint.
18. Regularity of sets with quasiminimal boundary surfaces in metric spaces, (with Juha Kinnunen, Andrew Lorent and Nageswari Shanmugalingam). J. Geom. Anal. 23 (2013), no. 4, 1607-1640. Preprint.
19. On Whitney-type characterization of approximate differentiability on metric measure spaces, (with Estibalitz Durand-Cartagena, Lizaveta Ihnatsyeva and Marta Szumańska). Canad. J. Math. (66) 2014, 721-742. Preprint.
20. Relative isoperimetric inequalitites and sufficient conditions for finite perimeter on metric spaces, (with Panu Lahti). Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 1, 129-154.
21. Pointwise properties of functions of bounded variation in metric spaces, (with Juha Kinnunen, Nageswari Shanmugalingam and Heli Tuominen). Rev. Mat. Complut. 27 (2014), no. 1, 41-67. Preprint.
22. A characterization of BMO self-maps of a metric measure space, (with Juha Kinnunen, Niko Marola, and Nageswari Shanmugalingam). Collect. Math. (2015) 66:405-421. Preprint in arXiv.
23. Smoothness spaces of higher order on lower dimensional subsets of the Euclidean space, (with Lizaveta Ihnatsyeva). Math. Nachr. 288, No. 11-12, 1303-1316 (2015). Preprint in arXiv.
24. Semmes family of curves and a characterization of functions of bounded variation in terms of curves, (with Panu Lahti and Nageswari Shanmugalingam). Calc. Var. Partial Differential Equations 54 (2015), no. 2, 1393-1424. Preprint in CVGMT.
25. Stability and continuity of functions of least gradient, (with Heikki Hakkarainen, Panu Lahti and Nageswari Shanmugalingam). Anal. Geom. Metr. Spaces 3 (2015), 123-139. Preprint in arXiv.
26. Homeomorphisms of the Heisenberg group preserving BMO, (with Niko Marola and Olli Saari). Arch. Math. (Basel) 106 (2016), no. 2, 175-182. Preprint.
27. Minima of quasisuperminimizers, (with Anders Björn and Jana Björn) Preprint in arXiv. Nonlinear Anal. 155 (2017) 264-284.
28. The space JN_p: nontriviality and duality, (with Galia Dafni, Tuomas Hytönen, Hong Yue). J. Funct. Anal. 275 (2018), no. 3, 577-603. Preprint in arXiv.
29. The higher integrability of weak solutions of porous medium systems, (with Verena Bögelein, Frank Duzaar and Christoph Scheven). Adv. Nonlinear Anal., 2019. Preprint.
30. Notions of Dirichlet problem for functions of least gradient in metric measure spaces , (with Panu Lahti, Xining Li and Nageswari Shanmugalingam). Revista Matematica Iberoamericana, 2019. Preprint in arXiv.
31. Lower semicontinuous obstacles for the porous medium equation, (with Pekka Lehtelä, Stefan Sturm). J. Differential Equations, 2019. Preprint in arXiv.
32. A maximal function approach to two-measure Poincaré inequalities, (with Juha Kinnunen, Juha Lehrbäck and Antti V. Vähäkangas). The Journal of Geometric Analysis, 2019. Preprint in arXiv.
33. Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality, (with Estibalitz Durand-Cartagena, Sylvester Eriksson-Bique and Nageswari Shanmugalingam). Advances in Calculus of Variations, 2019. Preprint in arXiv.
34. Regularity of Solutions to the Fractional Cheeger-Laplacian on Domains in Metric Spaces of Bounded Geometry (with Sylvester Eriksson-Bique, gianmarco giovannardi, Nageswari Shanmugalingam and Gareth Speight) Journal of Differential Equations, 2022.
35. Accessible parts of the boundary for domains in metric measure spaces
(with Ryan Gibara). Annales Fennici Mathematici, 2022. Preprint in arXiv.
36. Solving a Dirichlet problem on unbounded domains via a conformal transformation (with Ryan Gibara and Nageswari Shanmugalingam). Math. Annalen (to appear) arXiv.
37. The John-Nirenberg space: Equality of the vanishing subspaces VJN_p and CJN_p (with Timo Takala). J. Geom. Anal. (to appear). Preprint in arXiv.

Submitted papers

38. Neumann problems for p-harmonic functions, and induced nonlocal operators in metric measure spaces (with Luca Capogna, Josh Kline, Nageswari Shanmugalingam and Marie Snipes). Preprint in arXiv.
39. Traces of Newton-Sobolev functions on the visible boundary of domains in doubling metric measure spaces supporting a p-Poincaré inequality (with Sylvester Eriksson-Bique, Ryan Gibara and Nageswari Shanmugalingam). Preprint in arXiv
40. Sharp Hausdorff content estimates for accessible boundaries of domains in metric measure spaces of controlled geometry (with Sylvester Eriksson-Bique, Ryan Gibara and Nageswari Shanmugalingam). Preprint in arXiv

Theses

• Geometric properties of metric measure spaces and Sobolev-type inequalities, PhD thesis, Helsinki University of Technology, 2008.
• Geometric implications of the Poincaré inequality, Licentiate's thesis, Helsinki University of Technology, 2006.
• Poincarén epäyhtälö metrisissä avaruuksissa, Master's thesis (in Finnish), Helsinki University of Technology, 2004.

Other

• Leikki metrisessä avaruudessa kannustaa luovuuteen, (with Outi Elina Maasalo), popular article (in Finnish), Arkhimedes 4/2008. Kopio.