Publications

Preprint

  • Discontinuous eikonal equations in metric measure spaces, (joint with Q. Liu and N. Shanmugalingam), arXiv. 

  • Green functions in metric measure spaces, (joint with M. Bonk and L. Capogna), arXiv.

  • A characterization of BV and Sobolev functions via nonlocal functionals in metric spaces, (joint with P. Lahti and A. Pinamonti), arXiv.

  • Metric quasiconformality and Sobolev regularity in non-Ahlfors regular spaces, (joint with P. Lahti), arXiv

  • Quasiconformal and Sobolev mappings in non-Ahlfors regular metric spaces, (joint with P. Lahti), arXiv

Publication​​

  1. Sobolev embedding on a sphere containing an arbitrary Cantor set in the image, (with P. Hajlasz), Geom. Dedicata. 184 (2016), 159--173. arXiv  

  2. A game-theoretic proof of convexity preserving properties for motion by curvature, (with Q. Liu and A. Schikorra), Indiana Univ. Math. J. 65 (2016), 171--197. PDF file

  3. Lipschitz continuity and convexity preserving for solutions of semilinear evolution equations in the Heisenberg group, (with Q. Liu and J. J. Manfredi), Calc. Var. Partial Differential Equations 55 (2016), no.4, Art. 80, 25pp. arXiv

  4. Sobolev functions in the critical case are uniformly continuous in s-Ahlfors regular metric spaces when s less than or equal to one, Proc. Amer. Math. Soc. 145 (2017), no. 1, 267-272. arXiv

  5. Weakly coupled systems of fully nonlinear parabolic equations in the Heisenberg group, (with Q. Liu), Nonlinear Anal. 174 (2018), 54-78. PDF file

  6. Strong comparison principle for p-harmonic functions in Carnot-Caratheodory spaces, (with L. Capogna), Proc. Amer. Math. Soc. 146 (2018), no. 10, 4265-4274.  arXiv

  7. Absolutely continuous functions on compact and connected one-dimensional metric spaces, Ann. Acad. Sci. Fenn. Math. Volumen 44, (2019), 281-291. PDF file

  8. Horizontal convex envelope in the Heisenberg group and applications to sub-elliptic equations, (with Q. Liu),  Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 22 (2021), no. 4, 2039–2076. arXiv

  9. Functions of bounded variation on complete and connected one-dimensional metric spaces, (with P. Lahti), Int. Math. Res. Not. IMRN 2021, no. 20, 15412–15443.  arXiv

  10. Equivalence of solutions of eikonal equation in metric spaces, (joint with Q. Liu and N. Shanmugalingam), J. Differential Equations 272 (2021), 979–1014. arXiv 

  11. Differential games and Hamilton-Jacobi-Isaacs equations in metric spaces, (with Q. Liu), accepted by Minimax Theory and its Applications.

  12. Absolutely continuous mappings on doubling metric measure spaces, (joint with P. Lahti), accepted by Manuscripta Mathematica, arXiv

  13. Horizontally quasiconvex envelope in the Heisenberg group, (joint with A. Kijowski and Q. Liu), submitted, accepted by Rev. Mat. Iberoam.,  arXiv

Lecture Notes

  • Hamilton-Jacobi equations in metric spaces, (joint with Q. Liu), (notes for our minicourse at OIST Summer Graduate School "Analysis and Partial Differential Equations" on June 12-17, 2023) arXiv