Carta conforme con minime deformazioni areali. Nota I

Fernando Sansò

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1972)

  • Volume: 52, Issue: 2, page 197-205
  • ISSN: 0392-7881

Abstract

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The problem we investigate concerns the choice, among conformal cartographic representations, of the one that causes as small areal deformations as possible. To that aim, we define an index of the global areal deformation through a functional T depending on the form of the cartographic representation. Since conformal representations are realized by a couple of harmonic functions, one of which depends on the other, we introduce a suitable topological space E of harmonic functions. The problem now becomes the minimization of the functional T of the space E. In this paper a theorem of existence of the minimum of T on E is demonstrated by means of classic variational techniques.

How to cite

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Sansò, Fernando. "Carta conforme con minime deformazioni areali. Nota I." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 52.2 (1972): 197-205. <http://eudml.org/doc/295848>.

@article{Sansò1972,
author = {Sansò, Fernando},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
language = {ita},
month = {2},
number = {2},
pages = {197-205},
publisher = {Accademia Nazionale dei Lincei},
title = {Carta conforme con minime deformazioni areali. Nota I},
url = {http://eudml.org/doc/295848},
volume = {52},
year = {1972},
}

TY - JOUR
AU - Sansò, Fernando
TI - Carta conforme con minime deformazioni areali. Nota I
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1972/2//
PB - Accademia Nazionale dei Lincei
VL - 52
IS - 2
SP - 197
EP - 205
LA - ita
UR - http://eudml.org/doc/295848
ER -

References

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  1. JORDAN, e EGGERT, , Handbuch der Vermessungskunde Driker band, Zweiter Halbband, J. B. Metzlersche Verlagsbuchhandlung, Stuttgart1941. 
  2. HOTINE, MARTIN, Mathematical Geodesy. U. S. Department of Commerce, Environmental Science Services Administration, Washington D. C.1969. 
  3. RIESZ, e NAGY, , Leçons d'analyse fonctionnelle. Gauthiers Villars, Paris1965. Zbl0122.11205MR179567
  4. BERGE, CLAUDE, Espaces topologiques, «Fonctions multivoques». Dunod, Paris1966. Zbl0088.14703MR105663

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