Affine Bernstein problems and Monge-Ampere equations:
In 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...
Gespeichert in:
| Format: | Elektronisch E-Book |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2010
|
| Schlagworte: | |
| Online-Zugang: | FHN01 Volltext |
| Zusammenfassung: | In 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 |
| Beschreibung: | xii, 180 p. ill |
| ISBN: | 9789812814173 |
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| 520 | |a In 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 | ||
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| id | DE-604.BV044636394 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:49Z |
| institution | BVB |
| isbn | 9789812814173 |
| language | English |
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| physical | xii, 180 p. ill |
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| publishDate | 2010 |
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| spelling | Affine Bernstein problems and Monge-Ampere equations An-Min Li ... [et al.] Singapore World Scientific Pub. Co. c2010 xii, 180 p. ill txt rdacontent c rdamedia cr rdacarrier In 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 Affine differential geometry Monge-Ampere equations Monge-Ampère-Differentialgleichung (DE-588)4253327-2 gnd rswk-swf Globale Differentialgeometrie (DE-588)4021286-5 gnd rswk-swf Monge-Ampère-Differentialgleichung (DE-588)4253327-2 s Globale Differentialgeometrie (DE-588)4021286-5 s 1\p DE-604 Li, An-Min 1946- Sonstige oth Erscheint auch als Druck-Ausgabe 9789812814166 Erscheint auch als Druck-Ausgabe 9812814167 http://www.worldscientific.com/worldscibooks/10.1142/6835#t=toc Verlag URL des Erstveroeffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Affine Bernstein problems and Monge-Ampere equations Affine differential geometry Monge-Ampere equations Monge-Ampère-Differentialgleichung (DE-588)4253327-2 gnd Globale Differentialgeometrie (DE-588)4021286-5 gnd |
| subject_GND | (DE-588)4253327-2 (DE-588)4021286-5 |
| title | Affine Bernstein problems and Monge-Ampere equations |
| title_auth | Affine Bernstein problems and Monge-Ampere equations |
| title_exact_search | Affine Bernstein problems and Monge-Ampere equations |
| title_full | Affine Bernstein problems and Monge-Ampere equations An-Min Li ... [et al.] |
| title_fullStr | Affine Bernstein problems and Monge-Ampere equations An-Min Li ... [et al.] |
| title_full_unstemmed | Affine Bernstein problems and Monge-Ampere equations An-Min Li ... [et al.] |
| title_short | Affine Bernstein problems and Monge-Ampere equations |
| title_sort | affine bernstein problems and monge ampere equations |
| topic | Affine differential geometry Monge-Ampere equations Monge-Ampère-Differentialgleichung (DE-588)4253327-2 gnd Globale Differentialgeometrie (DE-588)4021286-5 gnd |
| topic_facet | Affine differential geometry Monge-Ampere equations Monge-Ampère-Differentialgleichung Globale Differentialgeometrie |
| url | http://www.worldscientific.com/worldscibooks/10.1142/6835#t=toc |
| work_keys_str_mv | AT lianmin affinebernsteinproblemsandmongeampereequations |