Complete and Compact Minimal Surfaces

ISBN-13: 9789401069472 / Angielski / Miękka / 2011 / 188 str.

Kichoon Yang

Opis

'Et moi, ..., si j'avait su comment en reveni.r, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non- 111e series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Spis treści

I. Complete Minimal Surfaces in Rn.- §1. Intrinsic Surface Theory.- §2 Immersed Surfaces in Euclidean Space.- §3. Minimal Surfaces and the Gauss Map.- §4. Algebraic Gauss Maps.- §5. Examples.- §6. Minimal Immersions of Punctured Compact Riemann Surfaces.- §7. The Bernstein—Osserman Theorem.- II. Compact Minimal Surfaces in Sn.- §1. Moving Frames.- §2. Minimal Two—Spheres in Sn.- §3. The Twistor Fibration.- §4. Minimal Surfaces in ?P1.- §5. Examples.- III. Holomorphic Curves and Minimal Surfaces in CPn.- §1. Hermitian Geometry and Singular Metrics on a Riemann Surface.- §2. Holomorphic Curves in ?Pn.- §3. Minimal Surfaces in a Kahler Manifold.- §4. Minimal Surfaces Associated to a Holomorphic Curve.- IV. Holomorphic Curves and Minimal Surfaces in the Quadric.- §1 Immersed Holomorphic Curves in the Two—Quadric.- §2. Holomorphic Curves in Q2.- §3. Horizontal Holomorphic Curves in SO(m)—Flag Manifolds.- §4. Associated Minimal Surfaces.- §5 Minimal Surfaces in the Quaternionic Projective Space.- V. The Twistor Method.- §1. The Hermitian Symmetric Space SO(2n)/U(m).- §2. The Orthogonal Twistor Bundle.- §3. Applications: Isotropic Surfaces and Minimal Surfaces.- §4. Self—Duality in Riemannian Four—Manifolds.