000			02496 a2200265 4500
008			240615b |||||||| |||| 00| 0 eng d
020			_a9781470476175
082			_a516.36 CIE
100			_aCieliebak, K.
245			_aIntroduction to the h-principle
250			_a2nd ed.
260			_aProvidence, Rhode Island: _bAmerican Mathematical Society, _c2024.
300			_axvii, 363p.: _bill.; pbk.: _c25cm.
440			_aGraduate Studies in Mathematics, Vol. 239
520			_aIn differential geometry and topology one often deals with systems of partial differential equations, as well as partial differential inequalities, that have infinitely many solutions whatever boundary conditions are imposed. It was discovered in the fifties that the solvability of differential relations (i.e. equations and inequalities) of this kind can often be reduced to a problem of a purely homotopy-theoretic nature. One says in this case that the corresponding differential relation satisfies the h -principle. Two famous examples of the h -principle, the Nash-Kuiper C1 -isometric embedding theory in Riemannian geometry and the Smale-Hirsch immersion theory in differential topology, were later transformed by Gromov into powerful general methods for establishing the h -principle. The authors cover two main methods for proving the h -principle: holonomic approximation and convex integration. The reader will find that, with a few notable exceptions, most instances of the h -principle can be treated by the methods considered here. A special emphasis in the book is made on applications to symplectic and contact geometry. Gromov's famous book “Partial Differential Relations”, which is devoted to the same subject, is an encyclopedia of the h -principle, written for experts, while the present book is the first broadly accessible exposition of the theory and its applications. The book would be an excellent text for a graduate course on geometric methods for solving partial differential equations and inequalities. Geometers, topologists and analysts will also find much value in this very readable exposition of an important and remarkable topic. https://bookstore.ams.org/gsm-48
650			_aGeometry
650			_aDifferential
650			_aDifferentiable Manifolds
650			_aThom Transversality Theorem
650			_aMaths
650			_aHomotopy Principle
700			_aEliashberg, Y. _eCo-author
700			_aMishachev, N. _eCo-author
942			_cTD _2ddc
999			_c60023 _d60023