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.
- 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).
- 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 L1, joint with Chris Gartland, Enrico Le Donne, Lisa Naples and Sebastiano Nicolussi-Golo, accepted to IMRN, available as preprint (arXiv: 2112.11402).
- 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 S2, 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.