Minimal Surfaces I is an introduction to the field of minimal surfaces and a presentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students who want to enter this interesting area of analysis and differential geometry which during the last 25 years of mathematical research has been very active and productive. Surveys of various subareas will lead the student to the current frontiers of knowledge and can also be useful to the researcher. The lecturer can easily base courses of one or two semesters on differential geometry on Vol. 1, as many topics are worked out in great detail. Numerous computer-generated illustrations of old and new minimal surfaces are included to support intuition and imagination. Part 2 leads the reader up to the regularity theory for nonlinear elliptic boundary value problems illustrated by a particular and fascinating topic. There is no comparably comprehensive treatment of the problem of boundary regularity of minimal surfaces available in book form. This long-awaited book is a timely and welcome addition to the mathematical literature.(paquot;, pa, pa#39;), paquot;(w):= (yaquot;(w) a oa)aamp;*(w) for w e BU I. Then the test vector % is admissible in (34), and we obtain ac 1 ... the absolute value of the second term of the left-hand side of (35) can be bounded from above by #| |VY|***dudv, 4 JB if we ... modulus of continuity of X. Hence there is a number K2 agt; 0 such that | |VY|* dudv alt; | aamp;*|WYa#39;dudv (36) S-(wo) S2a#39;-(wo) alt; K2 r * | |Y a ala dudv T2r holds for all re (0, p1).

Title | : | Minimal Surfaces II |

Author | : | Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab |

Publisher | : | Springer Science & Business Media - 2013-03-14 |

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