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Research interests:

Differential geometry: submanifolds of homogeneous spaces, geometric applications of exterior differential systems, the method of moving frames, integrable systems.
Mathematics of liquid crystals: Q-tensor theory, Q-tensor models and Landau-de Gennes energy of nematic liquid crystals.

Recent publications

Books and monographs:

G. R. Jensen, E. Musso, L. Nicolodi, Surfaces in Classical Geometries. A treatment by Moving Frames, Universitext, Springer, 2016, xiii + 571 pp., ISBN 978-3-319-27076-0.

Submitted papers:

O. Eshkobilov, E. Musso, L. Nicolodi, The geometry of conformal timelike geodesics in the Einstein universe, preprint, 2019.
E. Musso, L. Nicolodi, F. Salis, On the Cauchy-Riemann geometry of transversal curves in the 3-sphere, arXiv:2004.11350 [math.DG].

Published or accepted papers:

O. Eshkobilov, E. Musso, L. Nicolodi, On the restricted conformal group of the (1+n)-Einstein static universe, Journal of Geometry and Physics 146 (2019), 103517. DOI: 10.1016/j.geomphys.2019.103517. Preprint version: arXiv:1909.08563 [math.DG].
O. Eshkobilov, E. Musso, L. Nicolodi, Critical Robertson-Walker universes, Differential Geometry and its Applications 66 (2019), 23-41. DOI: 10.1016/j.difgeo.2019.05.008. Preprint version: arXiv:1904.08862 [math.DG].
E. Musso, L. Nicolodi, Topologically embedded helicoidal pseudospherical cylinders, Nonlinearity 32 (2019), no. 1, 22-45. DOI: 10.1088/1361-6544/aae720. Preprint version: arXiv:1707.09481 [math.DG].
E. Musso, L. Nicolodi, Surfaces in Laguerre Geometry, Banach Center Publications 117 (2019), 223-255. DOI: 10.4064/bc117-8.
G. R. Jensen, E. Musso, L. Nicolodi, Compact surfaces with no Bonnet mate, The Journal of Geometric Analysis 28 (2018), no. 3, 2644-2652. DOI: 10.1007/s12220-017-9924-y. Preprint version: arXiv:1703.09629 [math.DG].
D. Mucci, L. Nicolodi, On the Landau-de Gennes elastic energy of a Q-tensor model for soft biaxial nematics, Journal of Nonlinear Science 27 (2017), no. 6, 1687-1724. DOI: 10.1007/s00332-017-9383-4. Preprint version: http://cvgmt.sns.it/paper/3196/.
E. Musso, L. Nicolodi, Quantization of the conformal arclength functional on space curves, Communications in Analysis and Geometry 25 (2017), no. 1, 209-242. DOI: 10.4310/CAG.2017.v25.n1.a7. Preprint version: arXiv:1501.04101 [math.DG].
J. M. Manzano, E. Musso, L. Nicolodi, Bjoerling type problems for elastic surfaces, Rend. Semin. Mat. Univ. Politec. Torino 74 (2016), no. 1-2, 213-233. Reprint.
E. Musso, L. Nicolodi, Holomorphic differentials and Laguerre deformation of surfaces, Mathematische Zeitschrift 284 (2016), no. 3-4, 1089-1110; DOI: 10.1007/s00209-016-1689-7. Preprint version: arXiv:1401.1776 [math.DG].
A. Dzhalilov, E. Musso, L. Nicolodi, Conformal geometry of timelike curves in the (1+2)-Einstein universe, Nonlinear Analysis 143 (2016), 224-255; DOI: 10.1016/j.na.2016.05.011. Preprint version: arXiv:1603.01035 [math.DG].
D. Mucci, L. Nicolodi, On the Landau-de Gennes elastic energy of constrained biaxial nematics, SIAM Journal on Mathematical Analysis 48 (2016), no. 3, 1954-1987; DOI: 10.1137/15M1041043. Preprint version: http://cvgmt.sns.it/paper/2925/.
A. Altavilla, L. Nicolodi, On the volume of the Sp(n)Sp(1) shadow of a compact set, C. R. Math. Acad. Sci. Paris 354 (2016), 307-311; DOI: 10.1016/j.crma.2015.12.007.
E. Musso, L. Nicolodi, Marginally outer trapped surfaces in de Sitter space by low-dimensional geometries, Journal of Geometry and Physics 96 (2015), 168-186; DOI: 10.1016/j.geomphys.2015.06.009. Preprint version: pdf.
G. R. Jensen, E. Musso, L. Nicolodi, The geometric Cauchy problem for the membrane shape equation, Journal of Physics A: Mathematical and Theoretical 47 (2014), no. 49, 495201-22; DOI: 10.1088/1751-8113/47/49/495201. Chosen as an "IOP Select" article. Preprint version: arXiv:1406.5981 [math.DG].
E. Musso, L. Nicolodi, On Small-type formulae for curves in PSL(2,C), Rendiconti Lincei - Matematica e Applicazioni 24 (2013), no. 3, 311-328; DOI: 10.4171/RLM/656. Preprint version: pdf.
L. Nicolodi, Models for biaxial nematic liquid crystals, Journal of Physics: Conference Series 410 (2013) 012043; DOI: 10.1088/1742-6596/410/1/012043.
D. Mucci, L. Nicolodi, On the elastic energy density of constrained Q-tensor models for biaxial nematics, Archive for Rational Mechanics and Analysis 206 (2012), no. 3, 853-884; DOI: 10.1007/s00205-012-0543-2. Preprint version: http://cvgmt.sns.it/paper/1676/.
E. Musso, L. Nicolodi, Hamiltonian flows on null curves, Nonlinearity 23 (2010), 2117-2129; DOI: 10.1088/0951-7715/23/9/005. Preprint version: arXiv:0911.4467.
E. Musso, L. Nicolodi, Symplectic applicability of Lagrangian surfaces, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 5 (2009), 067, 18 pages; DOI: 10.1137/070686470; available as arXiv:0906.5607. (Contribution to the Special Issue “Elie Cartan and Differential Geometry”.)
E. Musso, L. Nicolodi, Invariant signature of closed planar curves, Journal of Mathematical Imaging and Vision 35 (2009), no. 1, 68-85; DOI: 10.1007/s10851-009-0155-0. Preprint version: pdf.
E. Musso, L. Nicolodi, Conformal deformation of spacelike surfaces in Minkowski space, Houston Journal of Mathematics 35 (2009), no. 4, 68-85. Preprint version: arXiv:0712.0807v1.
E. Musso, L. Nicolodi, The spinor representation of CMC 1 surfaces in hyperbolic space, in "Recent advances in Differential Geometry, International Conference in honour of Prof. O. Kowalski", Lecce (Italy), June 13-16, 2007, Note di Matematica 28 (2008), suppl. n. 1, 317-339. Preprint version: pdf. DOI: 10.1285/i15900932v28n1supplp317.
E. Musso, L. Nicolodi, Reduction for constrained variational problems on 3D null curves, SIAM Journal on Control and Optimization 47 (2008), no. 3, 1399-1414; DOI: 10.1137/070686470. Preprint version: arXiv:0710.0483v1.
E. Musso, L. Nicolodi, Closed trajectories of a particle model on null curves in anti-de Sitter 3-space, Classical and Quantum Gravity 24 (2007) 5401-5411. Preprint version: arXiv:0709.2017v1.
E. Musso, L. Nicolodi, Differential systems associated with tableaux over Lie algebras, "Symmetries and Overdetermined Systems of Partial Differential Equations", 497-514, The IMA Volumes in Mathematics and its Applications, 144, Springer, New York, 2008. Preprint version: arXiv:0705.2715v1.
E. Musso, L. Nicolodi, A class of overdetermined systems defined by tableaux: Involutiveness and Cauchy problem, Physica D: Nonlinear Phenomena 229 (2007), no. 1, 35-42. DOI: 10.1016/j.physd.2007.03.010. Preprint version: math.DG/0602676.
E. Musso, L. Nicolodi, Tableaux over Lie algebras, integrable systems, and classical surface theory, Communications in Analysis and Geometry 14 (2006), no. 3, 475-496. Preprint version: math.DG/0412169.
L. Nicolodi, L. Vanhecke, The geometry of k-harmonic manifolds, Advances in Geometry 6 (2006), 53-70. DOI: 10.1515/ADVGEOM.2006.004.
E. Musso, L. Nicolodi, Deformation and applicability of surfaces in Lie sphere geometry, Tohoku Mathematical Journal 58 (2006), 161-187. Preprint version: math.DG/0408009.
E. Musso, L. Nicolodi, On the Cauchy problem for the integrable system of Lie minimal surfaces, Journal of Mathematical Physics 46 (2005), no. 11, 3509-3523. DOI: 10.1063/1.2116267.
E. Musso, L. Nicolodi, Reduction for the projective arclength functional, Forum Mathematicum 17 (2005), 569-590. DOI: 10.1515/form.2005.17.4.569.
E. Musso, L. Nicolodi, Darboux transforms of Dupin surfaces, Banach Center Publications 57 (2002), 135-154.
E. Musso, L. Nicolodi, Special isothermic surfaces and solitons, Contemp. Math. 288 (2001), 129-148. Preprint version:math.DG/0108170.
U. Hertrich-Jeromin, E. Musso, L. Nicolodi, Moebius geometry of surfaces of constant mean curvature 1 in hyperbolic space, Ann. Global Anal. Geom. 19 (2001), 185-205. DOI: 10.1023/A:1010738712475. Preprint version: math.DG/9810157.
E. Musso, L. Nicolodi, The Bianchi--Darboux transform of L-isothermic surfaces, Internat. J. Math. 11 (2000), 911-924. DOI: 10.1142/S0129167X00000465. Preprint version: math.DG/0001062.
L. Nicolodi, The Calapso and Bianchi-Darboux transformations of L-isothermic surfaces, in Atti del Congresso Internazionale di Geometria Differenziale in onore di Pasquale Calapso, Messina, Ottobre 1998, Rend. Sem. Mat. Messina Ser. II, suppl. (2000), 257-266.
F. Burstall, U. Hertrich-Jeromin, L. Nicolodi, Curved flats and transformations, RiP report, Oberwolfach, 1999.
S. Console, L. Nicolodi, Infinitesimal characterization of almost Hermitian homogeneous spaces, Comment. Math. Univ. Carolin. 40 (1999), 713-721; link to the article.
E. Musso, L. Nicolodi, Willmore canal surfaces in Euclidean space, Rend. Istit. Mat. Univ. Trieste 31 (1999), 1-26; link to the article.
E. Musso, L. Nicolodi, Laguerre geometry of surfaces with plane lines of curvature, Abh. Math. Sem. Univ. Hamburg 69 (1999), 123-138. Preprint version: pdf.