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Geometric and Harmonic Analysis with Interdisciplinary Applications

Deliverables

minimal surfaces and geometric PDE

Two preprints will be obtained: one on geometric PDE (UNIBO-PU), one on minimal surfaces (UGR-PITTS).

Infinite dimensional representation

A preprint will be prepared (UNIBO - UC).

degenerate PDE

A preprint will be obtained on the regularity of solutions (UNIBO - MIT)

image analysis and vision

Three preprints will be prepared: one on geometrical cortical organization (CNRS-YALE), one on image analysis (UNIBO-UC-GMV,) one on stochastic propagation (CNRS-UNIBO-MIT).

reproducing kernel spaces and Fourier analysis

Two preprints will be obtained: one on on reproducing kernel Hilbert spaces (UNIBO - WU), one on restriction of the Fourier transform (UAM - UC).

sampling in group invariant spaces

A preprint will be obtained (UAM -UBA).

nonlocal and non linear PDE

Two preprints will be delivered: one on nonlocal diffusion (UAM-UT). One on p-Laplacian in Euclidean spaces (UAM-UBA).

Outreach presentations

Organization of outreach events, press releases, communication actions and web site, and development of a Communication Plan.

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Publications

Conformality and Q-harmonicity in Sub-Riemannian manifolds

Author(s): L. Capogna, G. Citti, E. Le Donne, A. Ottazzi,
Published in: cvgmt.sns.it, 2018

Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounded Domains

Author(s): Matteo Bonforte, Alessio Figalli
Published in: arxiv.org, 2019

From receptive profiles to a metric model of V1

Author(s): Noemi Montobbio, Giovanna Citti, Alessandro Sarti
Published in: arxiv.org, 2019

Lagrangian study of the final warming in the southern stratosphere during 2002: Part I. The Vortex Splitting at Upper Levels

Author(s): Jezabel Curbelo, Carlos R. Mechoso, Ana M. Mancho, Stephen Wiggins
Published in: arxiv.org, 2019

Neurogeometry of perception: isotropic and anisotropic aspects

Author(s): Giovanna Citti, Alessandro Sarti
Published in: arxiv.org, 2018

Conformality and Q -harmonicity in sub-Riemannian manifolds

Author(s): Luca Capogna, Giovanna Citti, Enrico Le Donne, Alessandro Ottazzi
Published in: Journal de Mathématiques Pures et Appliquées, 2017, ISSN 0021-7824
DOI: 10.1016/j.matpur.2017.12.006

Extending an Example by Colding and Minicozzi

Author(s): Lorenzo Ruffoni, Francesca Tripaldi
Published in: The Journal of Geometric Analysis, Issue 30/1, 2020, Page(s) 1028-1041, ISSN 1050-6926
DOI: 10.1007/s12220-019-00177-4

Nonlocal diffusion equations with dynamical boundary conditions

Author(s): Pablo M. Berná, Julio D. Rossi
Published in: Nonlinear Analysis, Issue 195, 2020, Page(s) 111751, ISSN 0362-546X
DOI: 10.1016/j.na.2020.111751

Lebesgue inequalities for Chebyshev thresholding greedy algorithms

Author(s): P. M. Berná, Ó. Blasco, G. Garrigós, E. Hernández, T. Oikhberg
Published in: Revista Matemática Complutense, 2019, ISSN 1139-1138
DOI: 10.1007/s13163-019-00328-9

Quantitative a priori estimates for fast diffusion equations with Caffarelli–Kohn–Nirenberg weights. Harnack inequalities and Hölder continuity

Author(s): Matteo Bonforte, Nikita Simonov
Published in: Advances in Mathematics, Issue 345, 2019, Page(s) 1075-1161, ISSN 0001-8708
DOI: 10.1016/j.aim.2019.01.018

Calderón-type inequalities for affine frames

Author(s): Davide Barbieri, Eugenio Hernández, Azita Mayeli
Published in: Applied and Computational Harmonic Analysis, 2019, ISSN 1063-5203
DOI: 10.1016/j.acha.2019.07.004

Asymptotic mapping class group of closed surfaces punctured along Cantor sets

Author(s): J. Aramayona, L. Funar
Published in: Moscow Mathematical Journal, 2017, ISSN 1609-3321

A Geometric Interpretation of Stochastic Gradient Descent Using Diffusion Metrics

Author(s): Rita Fioresi, Pratik Chaudhari, Stefano Soatto
Published in: Entropy, Issue 22/1, 2020, Page(s) 101, ISSN 1099-4300
DOI: 10.3390/e22010101

Correction to: From receptive profiles to a metric model of V1

Author(s): Noemi Montobbio, Giovanna Citti, Alessandro Sarti
Published in: Journal of Computational Neuroscience, Issue 47/2-3, 2019, Page(s) 231-231, ISSN 0929-5313
DOI: 10.1007/s10827-019-00728-2

Nonlocal diffusion equations with dynamical boundary conditions

Author(s): P.M. Berna, J. D. Rossi
Published in: Nonlinear Analysis, Theory, Methods and Applications, 2019, ISSN 0362-546X

Optimal translational-rotational invariant dictionaries for images

Author(s): Davide Barbieri, Carlos Cabrelli, Eugenio Hernández, Ursula Molter
Published in: Wavelets and Sparsity XVIII, 2019, Page(s) 3
DOI: 10.1117/12.2528890