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 cē 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