Calculus of Variations |
Contents
1 Definition of the Space | 2 |
The Notion of the Field and the Weierstrass EFunction | 29 |
Minimum Points and Conjugate Points | 85 |
1 other sections not shown
Common terms and phrases
accumulation point admissible curve arc length arc of class assumption class c² compact conjugate point connecting Consider const continuous function contradiction contravariant vector convergent coordinate neighborhood coordinate system covariant vector defined derivatives differential double point E-function Ep P(T equations essentially positive Euler equation Euler vector exists a neighborhood extremal arc field of extremals finite number given gradient greatest lower bound hence homeomorphic homotopic hyper-surfaces initial values integral lemma limit point manifold metric minimizing arc normal coordinates P₁ P₂ parameter point set points Q positive homogeneous proof relative minimum point second variation shown solution space sub-arc sufficiently small t₁ t₂ Take tangent tangent vector theorem vanishes vector field y₁ zero бе бхі نام