000			01839cam a22002657a 4500
003			CUTN
005			20171206144024.0
008			100803s2010 njua b 001 0 eng d
020			_a9789812814166
020			_a9812814167 (hbk.)
042			_alccopycat
082	0	4	_a516.36 _222 _bANM
100			_aAn-Min, Li
245	0	0	_aAffine Bernstein problems and Monge-Ampère equations / _cAn-Min Li ... [et al.].
260			_aHackensack, NJ : _bWorld Scientific, _cc2010.
300			_axii, 180 p. : _bill. ; _c26 cm.
500			_aIn this monograph, the interplay between geometry and partial differential equations (PDEs) is of particular interest. It gives a selfcontained introduction to research in the last decade concerning global problems in the theory of submanifolds, leading to some types of Monge-Ampere equations.From the methodical point of view, it introduces the solution of certain Monge-Ampere equations via geometric modeling techniques. Here geometric modeling means the appropriate choice of a normalization and its induced geometry on a hypersurface defined by a local strongly convex global graph. For a better understanding of the modeling techniques, the authors give a selfcontained summary of relative hypersurface theory, they derive important PDEs (e.g. affine spheres, affine maximal surfaces, and the affine constant mean curvature equation). Concerning modeling techniques, emphasis is on carefully structured proofs and exemplary comparisons between different modelings.
505			_aLocal Equiaffine Hypersurface Theory; Pogorelov's Theorem; Affine Maximal Hypersurfaces.
650		0	_aAffine differential geometry.
650		0	_aMonge-Ampère equations.
700	1		_aLi, An-Min,
942			_2ddc _cBOOKS
504			_aIncludes bibliographical references (p. 173-177) and index.
700	1		_d1946-
999			_c24192 _d24192