University of Jyväskylä

FI-40014 Finland

I am a postdoc at the Department of Mathematics and Statistics of the University of Jyväskylä in Finland (EU), under the supervision of Katrin Fässler.

Metric Geometry and Geometric Measure Theory, together with Lie Group Theory, are my main areas of research, with particular emphasis on problems that arise in sub-Riemannian Geometry, Analysis on Metric Spaces and in Harmonic Analysis.

Primarily, I study Lie groups equipped with non-Riemannian distances such as Carnot-Carathéodory distances. Carnot-Carathéodory Geometry, also called sub-Riemannian Geometry, deals with geometric spaces of fractal nature arising from several contexts, such as Hyperbolic Geometry, Geometric Group Theory, Theory of Hypoelliptic Operators and Control Theory.

In particular, I am interested in the regularity of minimal submanifolds, conditions for equivalence between CC distances and boundedness of certain operators. The recurrent theme is the geometry of Carnot groups, which appear in the asymptotic geometry of CC spaces, both at infinitesimal and at large scales.

I obtained a double PhD degree in 2017 from the University of Jyväskylä (Finland, EU) and from the University of Trento (Italy, EU), under the supervision of Enrico Le Donne and Francesco Serra Cassano. I later worked in Birmingham (UK) with Alessio Martini for one year, and in Padova (IT,EU) with Davide Vittone for one year and a half

If you want to know more about me, here is my CV. If you want to contact me, you can write me an email to sebastiano.s.nicolussi-golo@jyu.fi. My ORCID ID is: 0000-0002-3773-6471.

# Publications

### Preprints

• “Sub-Finsler horofunction boundaries of the Heisenberg group”
(with N. Fisher),
[arXiv]
• “Area-minimizing cones in the Heisenberg group $$\mathbb{H}^1$$”
(with M. Ritoré)
[arXiv]
• “Area of intrinsic graphs and coarea formula in Carnot Groups”
(with A. Julia and D. Vittone)
[arXiv] [cvgmt]
• “Intrinsic rectifiability via flat cones in the Heisenberg group”
(with A. Julia)
[arXiv] [cvgmt]
• “Polarised Lie groups contactomorphic to stratified groups”
(with A. Ottazzi)
[arXiv]
• “Spectral multipliers and wave equation for sub-Laplacians: lower bounds of Euclidean type”
(with A. Martini, D. Müller)
[arXiv]
• “Quasiregular mappings between subRiemannian manifolds”
(with C.-Y. Guo, M. Williams)
[arXiv]
• “From homogeneous metric spaces to Lie groups”
(with M. G. Cowling, V. Kivioja, E. Le Donne, A. Ottazzi )
[arXiv]

### Published papers

1. “Metric Lie groups admitting dilations”
(with E. Le Donne)
Accepted in Arkiv för Matematik (2020)
[arXiv] [cvgmt]
2. “The Bernstein problem for Lipschitz intrinsic graphs in the Heisenberg group”
(with F. Serra Cassano)
Calculus of Variations and Partial Differential Equations, 58,  141  (2019)
[Paper] [arXiv] [cvgmt]
3. “The Besicovitch covering property in the Heisenberg group revisited”
(with S. Rigot)
The Journal of Geometric Analysis 29, 3345–3383 (2019)
[Paper] [arXiv]
4. “Some remarks on contact variations in the first Heisenberg group”
Ann. Acad. Sci. Fenn. Math. 43, 311–335 (2018)
[Paper] [arXiv] [cvgmt]
5. “Regularity properties of spheres in homogeneous groups”
(with E. Le Donne)
Trans. Amer. Math. Soc., 370, 2057-2084 (2018).
[Paper] [arXiv] [cvgmt]
6. “Topics in the geometry of non-Riemannian lie groups”
PhD Thesis, University of Jyväskylä, 2017
[Online]
7. “Asymptotic behavior of the Riemannian Heisenberg group and its horoboundary”
(with E. Le Donne, A. Sambusetti)
Ann. Mat. Pura Appl. Volume 196, Issue 4, pp 1251–1272 (2017)
[Paper] [arXiv] [cvgmt]
8. “A historical account on characterizations of C^1-manifolds in Euclidean spaces by tangent cones”
(with F. Bigolin)
J. Math. Anal. Appl. 2014
[Paper]

# Collaborators

Francesco Bigolin
Michael G. Cowling
Moon Duchin
Nate Fisher
Chang-Yu Guo
Ville Kivioja
Enrico Le Donne
Alessio Martini
Detlef Müller
Alessandro Ottazzi
Séverine Rigot
Manuel Ritoré
Andrea Sambusetti
Raul Serapioni
Francesco Serra Cassano
Ben Warhurst
Marshall Williams