Enrico Giusti (born
Priverno Priverno is a town, ''comune'' in the province of Latina, Lazio, central Italy. It was called ''Piperno'' until 1927.
It has a station of the Rome-Naples railway mainline. Nearby is the Monti Lepini chain. It was the birthplace of the canonist Regi ...
, 1940), is an Italian mathematician mainly known for his contributions to the fields of
calculus of variations
The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions
and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...
, regularity theory of
partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function.
The function is often thought of as an "unknown" to be sol ...
s,
minimal surfaces
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below).
The term "minimal surface" is used because these surfaces originally arose as surfaces that ...
and
history of mathematics
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments ...
. He has been professor of mathematics at the
Università di Firenze
The University of Florence (Italian: ''Università degli Studi di Firenze'', UniFI) is an Italian public research university located in Florence, Italy. It comprises 12 schools and has around 50,000 students enrolled.
History
The first universi ...
;
he also taught and conducted research at the
Australian National University
The Australian National University (ANU) is a public research university located in Canberra, the capital of Australia. Its main campus in Acton encompasses seven teaching and research colleges, in addition to several national academies and ...
at Canberra, at the
Stanford University
Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is consider ...
and at the
University of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...
. After retirement, he devoted himself to the managing of the "Giardino di Archimede", a museum entirely dedicated to mathematics and its applications. Giusti is also the editor-in-chief of the international journal, dedicated to the history of mathematics "Bollettino di storia delle scienze matematiche".
One of the most famous results of Giusti, is the one obtained with
Enrico Bombieri
Enrico Bombieri (born 26 November 1940, Milan) is an Italian mathematician, known for his work in analytic number theory, Diophantine geometry, complex analysis, and group theory. Bombieri is currently Professor Emeritus in the School of Mathema ...
and
Ennio De Giorgi, concerning the minimality of
Simons Simons is a surname of Scandinavian origins and a variant of Sigmundsson, a patronymic surname with roots in proto-Germanic ''*segaz'' and ''*mundō'', giving a rough translation of "protection through victory".
Notable people
A
* Alan ...
' cones, and allowing to disprove the validity of
Bernstein's theorem in dimension larger than 8. The work on minimal surfaces was mentioned in the citation of the
Fields medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...
eventually awarded to Bombieri in 1974.
Giusti has a sustained interest in the history of mathematics, e.g. the mathematics of
Pierre de Fermat
Pierre de Fermat (; between 31 October and 6 December 1607 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he ...
(see Giusti 2009). He is the currently the director of the
Garden of Archimedes
The Garden of Archimedes (Italian: ''Il Giardino Di Archimede'') is a museum for mathematics in Florence, Italy. It was founded on March 26, 2004 and opened its doors to the public on April 14 of that year. The mission of the museum is to enhan ...
, a museum devoted to mathematics in Florence, Italy.
Il Giardino Di Archimede
EOS: IT solutions for the enterprise
Awards
Giusti won the Caccioppoli Prize The Caccioppoli Prize is awarded by the Italian Mathematical Union to an Italian mathematician not exceeding the age of 38 who established a wide international reputation. The prize is entitled to the memory of the Italian mathematician Renato Cacci ...
of the Italian Mathematical Union
The Italian Mathematical Union ( it, Unione Matematica Italiana) is a mathematical society based in Italy.
It was founded on December 7, 1922 by Luigi Bianchi, Vito Volterra, and most notably, Salvatore Pincherle, who became the Union's first Pr ...
in 1978
Selected publications
*"Minimal cones and the Bernstein problem
In differential geometry, Bernstein's problem is as follows: if the graph of a function on R''n''−1 is a minimal surface
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero m ...
" (with E. Bombieri e E. De Giorgi), Inventiones Mathematicae 7 (1969) 243–268
*"Harnack's inequality In mathematics, Harnack's inequality is an inequality relating the values of a positive harmonic function at two points, introduced by . Harnack's inequality is used to prove Harnack's theorem about the convergence of sequences of harmonic functions ...
for elliptic differential equations on minimal surfaces" (with E. Bombieri), Inventiones Mathematicae 15 (1972), 24–46
*
*.
*"On the equation of surfaces of prescribed mean curvature. Existence and uniqueness without boundary conditions", Inventiones Mathematicae 46 (1978), 111–137
*"On the regularity of the minima of variational integrals" (with M. Giaquinta), Acta Mathematica 148 (1982), 31–46
*"Differentiability of minima of nondifferentiable functionals" (with M. Giaquinta), Inventiones Mathematicae 72 (1983), 285–298
*"The singular set of the minima of certain quadratic functionals" (with M. Giaquinta), Annali della Scuola Normale Superiore di Pisa Classe di Scienze (Serie 4) 11 (1984), 45–55
*.
*, translated in English as .
*Giusti, Enrico, Les méthodes des maxima et minima de Fermat. Ann. Fac. Sci. Toulouse Math. (6) 18 (2009), Fascicule Spécial, 59–85.
See also
* Hilbert's nineteenth problem
*Plateau's problem
In mathematics, Plateau's problem is to show the existence of a minimal surface with a given boundary, a problem raised by Joseph-Louis Lagrange in 1760. However, it is named after Joseph Plateau who experimented with soap films. The problem ...
References
External links
Site of Caccioppoli Prize
{{DEFAULTSORT:Giusti, Enrico
21st-century Italian mathematicians
Living people
1940 births
PDE theorists
Variational analysts
University of Pisa faculty