Publications

Preprint

  • A second-order operator for horizontal quasiconvexity in the Heisenberg group and application to convexity preserving for horizontal curvature flow (joint with A. Kijowski, Q. Liu, Y. Zhang), arXiv.

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

  • 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.

Publication​​

16. Metric quasiconformality and Sobolev regularity in non-Ahlfors regular spaces, (joint with P. Lahti), Analysis and Geometry in Metric Spaces (to appear), arXiv

15. Quasiconformal and Sobolev mappings in non-Ahlfors regular metric spaces, (joint with P. Lahti), Tohoku Mathematical Journal (to appear), arXiv

14. A characterization of BV and Sobolev functions via nonlocal functionals in metric spaces, (joint with P. Lahti and A. Pinamonti), Nonlinear Analysis (to appear), arXiv. 

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

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

11. Differential games and Hamilton-Jacobi-Isaacs equations in metric spaces, (with Q. Liu), Minimax Theory and its Applications, 8 (2023), no. 1, 121–138.. PDF file.

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 

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

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

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

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

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

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

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

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