Bulletin of the American Mathematical Society

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Book Information:

Author: Francesco Maggi
Title: Sets of finite perimeter and geometric variational problems. An introduction to geometric measure theory
Additional book information: Cambridge Studies in Advanced Mathematics, Vol. 135, Cambridge University Press, Cambridge, 2012, xvii+454 pp., ISBN 978-1-107-02103-7, US $89.99

Frederick J. Almgren Jr. and Elliott H. Lieb, Singularities of energy minimizing maps from the ball to the sphere: examples, counterexamples, and bounds, Ann. of Math. (2) 128 (1988), no. 3, 483–530. MR 970609, DOI 10.2307/1971434

Enrico Bombieri, Régularité des hypersurfaces minimales, Séminaire Bourbaki. Vol. 1968/69: Exposés 347–363, Lecture Notes in Math., vol. 175, Springer, Berlin, 1971, pp. Exp. No. 353, 111–121 (French). MR 3077122

R. Caccioppoli, Sulle coppie di funzioni a variazione limitata, Rendiconti dell’Accademia di Scienze Fisiche e Matematiche di Napoli, 3 (in Italian) 34: 83-88, (1928).

Ennio De Giorgi, Su una teoria generale della misura $(r-1)$-dimensionale in uno spazio ad $r$ dimensioni, Ann. Mat. Pura Appl. (4) 36 (1954), 191–213 (Italian). MR 62214, DOI 10.1007/BF02412838

Ennio De Giorgi, Nuovi teoremi relativi alle misure $(r-1)$-dimensionali in uno spazio ad $r$ dimensioni, Ricerche Mat. 4 (1955), 95–113 (Italian). MR 74499

Ennio De Giorgi, Sulla proprietà isoperimetrica dell’ipersfera, nella classe degli insiemi aventi frontiera orientata di misura finita, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. Ia (8) 5 (1958), 33–44 (Italian). MR 98331

E. De Giorgi, Frontiere Orientate di Misura Minima, Seminario di Matematica della Scuola Normale Superiore di Pisa. Editrice Technico Scientifica, Pisa (1960).

Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325

P. Mattila, Fourier analysis and Hausdorff dimension (in preparation).

Christopher Marlowe, Dido, Queen of Carthage, circa 1593. Reprint available from Classic Reprint Series.

Frank Morgan, Geometric measure theory, 4th ed., Elsevier/Academic Press, Amsterdam, 2009. A beginner’s guide. MR 2455580

G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Annals of Mathematics Studies, No. 27, Princeton University Press, Princeton, N. J., 1951. MR 0043486

Robert Osserman, The isoperimetric inequality, Bull. Amer. Math. Soc. 84 (1978), no. 6, 1182–1238. MR 500557, DOI 10.1090/S0002-9904-1978-14553-4

F. White, Pressure Distribution in a Fluid, Fluid Mechanics. New York: McGraw-Hill. pp. 63-107, (2008).

• Frederick J. Almgren Jr. and Elliott H. Lieb, Singularities of energy minimizing maps from the ball to the sphere: examples, counterexamples, and bounds, Ann. of Math. (2) 128 (1988), no. 3, 483–530. MR 970609 (91a:58049), DOI 10.2307/1971434
• Enrico Bombieri, Régularité des hypersurfaces minimales, Séminaire Bourbaki. Vol. 1968/69: Exposés 347–363, Lecture Notes in Math., vol. 175, Springer, Berlin, 1971, pp. Exp. No. 353, 111–121 (French). MR 3077122
• R. Caccioppoli, Sulle coppie di funzioni a variazione limitata, Rendiconti dell’Accademia di Scienze Fisiche e Matematiche di Napoli, 3 (in Italian) 34: 83-88, (1928).
• Ennio De Giorgi, Su una teoria generale della misura $(r-1)$-dimensionale in uno spazio ad $r$ dimensioni, Ann. Mat. Pura Appl. (4) 36 (1954), 191–213 (Italian). MR 0062214 (15,945d)
• Ennio De Giorgi, Nuovi teoremi relativi alle misure $(r-1)$-dimensionali in uno spazio ad $r$ dimensioni, Ricerche Mat. 4 (1955), 95–113 (Italian). MR 0074499 (17,596a)
• Ennio De Giorgi, Sulla proprietà isoperimetrica dell’ipersfera, nella classe degli insiemi aventi frontiera orientata di misura finita, Atti Accad. Naz. Lincei. Mem. Cl. Sci. Fis. Mat. Nat. Sez. I (8) 5 (1958), 33–44 (Italian). MR 0098331 (20 \#4792)
• E. De Giorgi, Frontiere Orientate di Misura Minima, Seminario di Matematica della Scuola Normale Superiore di Pisa. Editrice Technico Scientifica, Pisa (1960).
• Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York Inc., New York, 1969. MR 0257325 (41 \#1976)
• P. Mattila, Fourier analysis and Hausdorff dimension (in preparation).
• Christopher Marlowe, Dido, Queen of Carthage, circa 1593. Reprint available from Classic Reprint Series.
• Frank Morgan, Geometric measure theory. A beginner’s guide, 4th ed., Elsevier/Academic Press, Amsterdam, 2009. MR 2455580 (2009i:49001)
• G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Annals of Mathematics Studies, no. 27, Princeton University Press, Princeton, N. J., 1951. MR 0043486 (13,270d)
• Robert Osserman, The isoperimetric inequality, Bull. Amer. Math. Soc. 84 (1978), no. 6, 1182–1238. MR 0500557 (58 \#18161)
• F. White, Pressure Distribution in a Fluid, Fluid Mechanics. New York: McGraw-Hill. pp. 63-107, (2008).