Andrea Colesanti - Research activity

Dipartimento di Matematica "U. Dini"
Viale Morgagni 67/A
50134 FIRENZE
tel. 055 2751464
colesant@math.unifi.it

Research interests

Recent papers

• A. Colesanti, D. Hug, E. Saorín-Gómez, Monotonicity and concavity of integral functionsl involving area measures of convex bodies, Communications in Contemporary Mathematics, 19, (2017), 26 pages.

• A. Colesanti, G. Livshyts, A. Marsiglietti, On the stability of Brunn-Minkowski type inequality,  Journal of Functional Analysis 273 (2017), 1120–1139.
  

• A. Colesanti, Log-concave functions, preprint, 2016.
  

• A. Colesanti, N. Lombardi, Valuations on the space of quasi-concave functions, preprint, 2015.

• A. Colesanti, K. Nystrom, P. Salani, J. Xiao, D. Yang, G. Zhang, The Hadamard variational formula and the Minkowski problem for p-capacity, Adv. Math. 285 (2015), 1511-1588.
  

• L. Cavallina, A. Colesanti, Monotone valuations on the space of convex functions, Analysis and Geometry in Metric Spaces, Vol. 1, issue 3, 2015 (electronic version). The paper is freely accesible on-line at  the  address:  http://dx.doi.org/10.1515/agms-2015-0012
  

• A. Colesanti, E. Saorín Gómez, J. Yepes Nicolás,  On a linear refinement of the Prékopa-Leindler inequality, Canadian Journal of Mathematics, 68(2016), no. 4, 762-783.. 
  

• A. Colesanti, D. Hug and E. Saorin-Gomez A characterization of some mixed volumes vie the Brunn-Minkowski inequality, Journal of Geometric Analysis (2012), pp. 1-28 (electronic version).

• S. Bobkov, A. Colesanti, I. Fragalŕ, Quermassintegrals of quasi-concave functions and generalized Prékopa-Leindler inequalities, Manuscripta Mathematica (2013), pp. 1-39 (electronic version).
  

• A. Colesanti, I. Fragalŕ The first variation of the total mass of log-concave functions and related inequalities. Advances in Mathematics 244 (2013), pp. 708-749.

• F. Barthe, C. Bianchini, A. Colesanti, Isoperimetry and Stability of Hyperplanes for Product Probability Measures. Annali di Matematica Pura e Applicata 192 (2) (2013), pp. 165-190.

• A. Colesanti, P. Manselli, Geometric and isoperimetric properties of sets of positive reach in ${\bf E}^d$. Atti del Seminario Matematico e Fisico dell'Universitŕ di Modena e Reggio Emilia, 57 (2010), 97-113.

• A. Colesanti, M. Fimiani, The Minkowski problem for torsional rigidity. Indiana University Mathematical Journal, 59 (2010) n. 3, 1013-1039.

• A. Colesanti, E. Saorin-Gomez, Functional inequalities derived from The Brunn-Minkowski inequality for quermassintegrals. J. Convex Anal. 17 (2010), n. 1, 35-49,

• L. Ambrosio, A. Colesanti, E. Villa, Outer Minkowski content for some classes of closed sets. Mathematische Annalen, 342 n.4 (2008), 727-748.

• A. Colesanti, From the Brunn-Minkowski inequality to a class of Poincare' type inequalities. Communications in Contemporary Mathematics, 10 n. 5 (2008), 765-772.

• C. Bianchini, A. Colesanti, A sharp Rogers-Shephard type inequality for the p-difference body of a planar convex body. Proceedings of the American Mathematical Society, 136 n. 7 (2008), 2575-2582.

• A. Colesanti, Functional inequalities related to the Rogers-Shephard inequality . Mathematika, 53 (2006), 81-101.

• A. Colesanti, P. Cuoghi and P. Salani, Brunn-Minkowski inequality for two functionals involving the p-Laplace operator. Applicable Analysis 85 1-3 (2006), 45-66.

• A. Colesanti and D. Hug, Hessian measures of convex functions and applications to area measures. Journal of the London Mathematical Society, (2) 71 (2005), 221-235.

• A. Colesanti, Brunn-Minkowski inequalities for variational problems and related problems. Advances in Mathematics, 194 (2005), 105-140.

• A. Colesanti and P. Cuoghi, The Brunn-Minkowski inequality for the n-dimensional logarithmic capacity. Potential Analysis 22 (2005), 289-304.

• A. Colesanti, On entire solutions of the Hessian equations $S_k(D^2 u)=1$. Quaderno del Dipartimento di Matematica "U. Dini", Universita' degli Studi di Firenze, 2004 (pdf).

• A. Colesanti and P. Salani, On the Brunn-Minkowski inequality for the p-capacity of convex bodies. Mathematische Annalen, 327 (2003), pp. 459-479.

• A. Colesanti and P. Salani, Quasi-concave envelope of a function and convexity of level sets of solutions to elliptic equations. Mathematische Nachrichten, 258 (2003), pp. 3-15.

Some recent talks and presentations

• Infinitesimal form of Brunn-Minkowski type inequalities, Conference "Convex and Discrete Geometry - On the occasion of Peter Gruber's 75th birthday, Vienna, July 4-8, 2016.

• On log-concave functions, Analytic tools in Probability and Applications, IMA, University of Minnesota, 2015.

• Around the Brunn-Minkowski inequality, Otto von Guericke Universitaet, Magdeburg and Technische Universitaet, Berlin, 2015

• Monotonicity and concavity of integral functionals defined on n-dimensional convex bodies, AMS Sectional Meeting,
  Session on High-Dimensional Convexity and Applications, San Francisco State University, October 2014
  

• Interactions between elliptic PDE's and convex geometry, The Cologne Conference on Nonlinear Differential Equations, On the occasion of Bernd Kawohl's sixtieth birthday, Cologne, 2013

• Functional notions of quermassintegrals, Interplay of convex geometry and Banach space theory, BIRS, Banff, 2013

• Functional versions of quermassintegrals, New trends in shape optimization, Centro di Ricerca Matematica Ennio De Giorgi, Pisa, 2012
  

• Hadamard's variational formulas for some functionals defined in the class of convex bodies, Shape optimization problems and spectral theory, CIRM, Luminy, 2012.

• The Minkowski problem and variations on the theme, Institut fur Mathematik, Osnabrueck, June, 2012.

• What is the perimeter of a log-concave function? Convexity and asymptotic geometric analysis, Centre de Recherches Mathematiques, Montreal, 2012.
  

• Derivatives of integrals of log-concave functions, Convex and integral geometry, Frankfurt, 2011

• Integral functionals verifying a Brunn-Minkowski type inequality, Asymptotic Geometric Analysis and Convexity, Toronto, 2010

• Minkowski type problems for variational functionals, Joint-Meeting of the AMS and the KMS, Seoul, 2009.
  

• The Minkowski problem for the torsional rigidity, 4th Annual Conference of the Network: Phenomena in High Dimensions, Sevilla, 2008

• On the one-sided Minkowski content of some classes of closed sets. Minikolloqium, Vienna, June 15th 2007.

• A sharp Rogers-Shephard type inequality for the p-difference body of a planar convex body, AMS Meeting - Hoboken, April 14-15, 2007.

• An infinitesimal form of Brunn-Minkowski type inequalities. This is a report of a talk given during the meeting 'Konvexgeometrie', Oberwolfach, 2006.