Harmonic Mappings in the Plane
ΠΌΠ°ΡΡ 2004β―Π³. Β· Cambridge Tracts in Mathematics ΠΠ½ΠΈΠ³Π°Β 156 Β· Cambridge University Press
ΠΠ»Π΅ΠΊΡΡΠΎΠ½Π½Π°Ρ ΠΊΠ½ΠΈΠ³Π°
212
ΠΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΡΡΡΠ°Π½ΠΈΡ
reportΠΡΠ΅Π½ΠΊΠΈ ΠΈ ΠΎΡΠ·ΡΠ²Ρ Π½Π΅ ΠΏΡΠΎΠ²Π΅ΡΠ΅Π½Ρ. ΠΠΎΠ΄ΡΠΎΠ±Π½Π΅Π΅β¦
ΠΠ± ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΠΎΠΉ ΠΊΠ½ΠΈΠ³Π΅
Harmonic mappings in the plane are univalent complex-valued harmonic functions of a complex variable. Conformal mappings are a special case where the real and imaginary parts are conjugate harmonic functions, satisfying the Cauchy-Riemann equations. Harmonic mappings were studied classically by differential geometers because they provide isothermal (or conformal) parameters for minimal surfaces. More recently they have been actively investigated by complex analysts as generalizations of univalent analytic functions, or conformal mappings. Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. Essentially self-contained, the book contains background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation. It is designed to introduce non-specialists to a beautiful area of complex analysis and geometry.
ΠΡΠ΅Π½ΠΈΡΠ΅ ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΡΡ ΠΊΠ½ΠΈΠ³Ρ
ΠΠΎΠ΄Π΅Π»ΠΈΡΠ΅ΡΡ Ρ Π½Π°ΠΌΠΈ ΡΠ²ΠΎΠΈΠΌ ΠΌΠ½Π΅Π½ΠΈΠ΅ΠΌ.
ΠΠ΄Π΅ ΡΠΈΡΠ°ΡΡ ΠΊΠ½ΠΈΠ³ΠΈ
Π‘ΠΌΠ°ΡΡΡΠΎΠ½Ρ ΠΈ ΠΏΠ»Π°Π½ΡΠ΅ΡΡ
Π£ΡΡΠ°Π½ΠΎΠ²ΠΈΡΠ΅ ΠΏΡΠΈΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅ Google Play ΠΠ½ΠΈΠ³ΠΈ Π΄Π»Ρ Android ΠΈΠ»ΠΈ iPad/iPhone. ΠΠ½ΠΎ ΡΠΈΠ½Ρ
ΡΠΎΠ½ΠΈΠ·ΠΈΡΡΠ΅ΡΡΡ Ρ Π²Π°ΡΠΈΠΌ Π°ΠΊΠΊΠ°ΡΠ½ΡΠΎΠΌ Π°Π²ΡΠΎΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈ, ΠΈ Π²Ρ ΡΠΌΠΎΠΆΠ΅ΡΠ΅ ΡΠΈΡΠ°ΡΡ Π»ΡΠ±ΠΈΠΌΡΠ΅ ΠΊΠ½ΠΈΠ³ΠΈ ΠΎΠ½Π»Π°ΠΉΠ½ ΠΈ ΠΎΡΠ»Π°ΠΉΠ½ Π³Π΄Π΅ ΡΠ³ΠΎΠ΄Π½ΠΎ.
ΠΠΎΡΡΠ±ΡΠΊΠΈ ΠΈ Π½Π°ΡΡΠΎΠ»ΡΠ½ΡΠ΅ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΡ
Π‘Π»ΡΡΠ°ΠΉΡΠ΅ Π°ΡΠ΄ΠΈΠΎΠΊΠ½ΠΈΠ³ΠΈ ΠΈΠ· Google Play Π² Π²Π΅Π±-Π±ΡΠ°ΡΠ·Π΅ΡΠ΅ Π½Π° ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ΅.
Π£ΡΡΡΠΎΠΉΡΡΠ²Π° Π΄Π»Ρ ΡΡΠ΅Π½ΠΈΡ ΠΊΠ½ΠΈΠ³
Π§ΡΠΎΠ±Ρ ΠΎΡΠΊΡΡΡΡ ΠΊΠ½ΠΈΠ³Ρ Π½Π° ΡΠ°ΠΊΠΎΠΌ ΡΡΡΡΠΎΠΉΡΡΠ²Π΅ Π΄Π»Ρ ΡΡΠ΅Π½ΠΈΡ, ΠΊΠ°ΠΊ Kobo, ΡΠΊΠ°ΡΠ°ΠΉΡΠ΅ ΡΠ°ΠΉΠ» ΠΈ Π΄ΠΎΠ±Π°Π²ΡΡΠ΅ Π΅Π³ΠΎ Π½Π° ΡΡΡΡΠΎΠΉΡΡΠ²ΠΎ. ΠΠΎΠ΄ΡΠΎΠ±Π½ΡΠ΅ ΠΈΠ½ΡΡΡΡΠΊΡΠΈΠΈ ΠΌΠΎΠΆΠ½ΠΎ Π½Π°ΠΉΡΠΈ Π² Π‘ΠΏΡΠ°Π²ΠΎΡΠ½ΠΎΠΌ ΡΠ΅Π½ΡΡΠ΅.
