Publications and Notes

Here is a list of the currently available preprints, publications and notes. If you just want to know about my research and projects, see the Research tab and the posts and overview there.

Preprints

- Tensorization of quasi-Hilbertian Sobolev spaces, joint with Elefterios Soultanis and Tapio Rajala, available as preprint (arXiv:2209.03040).
- Tensorization of p-weak differentiable structures, joint with Elefterios Soultanis and Tapio Rajala, (arXiv:2206.05046).
- Sylvester Eriksson-Bique,
*A New Hausdorff Content Bound for Limsup Sets*, available as preprint (arXiv:2201.13412).

Publications

- Density of Lipschitz functions in Energy, 2020, accepted to Calc. Var. & PDE.
- Infinitesimal splitting for spaces with thick curve families and Euclidean embeddings, joint with Guy C. David, 2020, accepted to Annales de l’institut Fourier.
*Nilpotent groups and biLipschitz embeddings into L*, joint with Chris Gartland, Enrico Le Donne, Lisa Naples and Sebastiano Nicolussi-Golo, accepted to IMRN, available as preprint (arXiv: 2112.11402).^{1}*Isoperimetric and Poincaré inequalities on non-self-similar Sierpiński sponges: the borderline case,*joint with Jasun Gong, accepted to Analysis and Geometry in Metric spaces, available as preprint (arXiv:2111.07861).*Bi-Lipschitz embeddings of quasiconformal trees,*joint with Vyron Vellis and Guy C. David, accepted to Proceedings of the AMS, available as preprint (arXiv:2106.13007).- Curvewise characterizations of minimal upper gradients and the construction of a Sobolev differential, joint with Elefterios Soultanis, accepted to Analysis and PDE, 2022.
*On Limits at Infinity of Weighted Sobolev Functions*, joint with Pekka Koskela and Khan Nguyen, Journal of Functional Analysis, Volume 283, Issue 10, 2022, 109672.- Regularity of Solutions to the Fractional Cheeger-Laplacian on Domains in Metric Spaces of Bounded Geometry, joint with Gianmarco Giovannardi, Riikka Korte, Nageswari Shanmugalingam, Gareth Speight, Journal of Differential Equations, 306, p. 590-632, 2022.
- Asymptotic behavior of BV functions and sets of finite perimeter in metric measure spaces. Joint with James T. Gill, Panu Lahti, Nageswari Shanmugalingam. Trans. Amer. Math. Soc., 374, p. 8201-8247, 2021.
- On the Sharp Lower Bound for Duality of Modulus, joint with Pietro Poggi-Corradini, accepted to Proc. Amer. Math. Soc., 2021.
- Almost uniform domains and Poincaré inequalities, joint with Jasun Gong, Transactions of the London Mathematical Society, 8(1), p. 243-298, 2021.
- Thin Loewner carpets and their quasisymmetric embeddings in S
^{2}, joint with Jeff Cheeger, accepted to Communications in Pure and Applied Mathematics, 2021. - Classifying Poincare inequalities and the local geometry of RNP-differentiability spaces, GAFA, 2019
- Regular mappings and non-existence of bi-Lipschitz embeddings for slit carpets, joint with Guy C David, Advances in Mathematics, 2019
- Self-improvement of weighted pointwise inequalities on open sets, joint with Juha Lehrbäck and Antti V. Vähäkangas, Journal of Functional Analysis, 2020
- Pointwise inequalities for Sobolev functions on outward cuspidal domains, joint with Pekka Koskela, Jan Maly and Zheng Zhu, IMRN, 2020.
- Self-improvement of pointwise Hardy inequality, joint with Antti V. Vähäkangas, Trans. Amer. Math. Soc.(2019)
- Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality, joint with Estibalitz Durand-Cartagena, Riikka Korte, Nageswari Shanmugalingam, Advances in Calculus of Variations 2019.
- Alternative proof of Keith-Zhong self-improvement and Conenctivity. Ann. Acad. Sci. Fenn. Alternative version with a different argument may be of interest, see here
- Quantitative Bi-Lipschitz embeddings of bounded curvature manifolds and orbifolds, Geometry and Topology 2018.
- Geometric k shortest paths, joint with J. Hershberger, V. Polishchuk, B. Speckmann, S. Suri, T. Talvitie, K. Verbeek, H. Yıldız. Soda 2015.
- Optimal geometric flows via dual programs, joint with V. Polishchuk, M. Sysikaski. SoCG 2014
- Optimization schemes for protective jamming, (minor contribution) joint with S. Sankararaman, K. Abu-Affash, A. Efrat, V. Polishchuk, S. Ramasubramanian, M. Segal. MobiHoc 2012.
- On Polygonal Paths with Bounded Discrete-Curvature: The Inflection-Free Case, joint with D. Kirkpatrick, V. Polishchuk. JCDCGG 2014.
- Importance Sampling for a Monte Carlo Matrix Multiplication Algorithm, with Application to Information Retrieval , coauthored with Mary Solbrig, Michael Stefanelli, Sarah Warkentin, Ralph Abbey and Ilse Ipsen.

Notes