New PDF release: Analytische Geometrie

By Pickert G.

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O} Then w r i t i n g t h e $I , we g e t But i t i s 6c[ From 1 . 5 . 1 , c dH n- + 24c6c -64 dHn = we d e r i v e , S and t h e n DIFFERENTIAL PROPERTIES OF SURFACES 26 such that j2*c'\x\-*dHn< This inequality holds for all @ . e. = 1x1 a In order to satisfy and 1x1 < 1 for $(x) and = I ~ 2 C 2 1 x \ - 2 d H nf < m lxlaCB for 1x1 > 1 . it is sufficient to choose a , such that 3! 4-n 2 4-n 2 a>---, a+p<-. For such a choice of $ ,a,p the inequality becomes 2 If we can choose a2 < 2 and (a+@)< 2 2c 0 .

2 , I 5 IDf(0) eW(O) 4 5 exp n > 2 . n = 2 . d. 7 BERNSTEIN THEOREM FOR FIVE DIMENSIONAL SURFACES B e r n s t e i n theorem i s t h e f o l l o w i n g c e l e b r a t e d r e s u l t , proved b y S . Bernstein if f(x) = a C 5 I or K61: f : R x 2 + -+ b R s o l v e s t h e minimal s u r f a c e e q u a t i o n , t h e n with aERL and bER . C. N i t s c h e C731, which r e d u c e d B e r n s t e i n ' s t o L i o n v i l l e ' s theorem f o r holomorphic f u n c t i o n s . H. Fleming K341 i n 1962.

D. 7 BERNSTEIN THEOREM FOR FIVE DIMENSIONAL SURFACES B e r n s t e i n theorem i s t h e f o l l o w i n g c e l e b r a t e d r e s u l t , proved b y S . Bernstein if f(x) = a C 5 I or K61: f : R x 2 + -+ b R s o l v e s t h e minimal s u r f a c e e q u a t i o n , t h e n with aERL and bER . C. N i t s c h e C731, which r e d u c e d B e r n s t e i n ' s t o L i o n v i l l e ' s theorem f o r holomorphic f u n c t i o n s . H. Fleming K341 i n 1962. Fleming a p p l i e d t o g l o b a l s o l u t i o n s o f minimal s u r f a c e e q u a t i o n t h e newly developed methods of Geometric Measure Theory, t o o b t a i n a new p r o o f of B e r n s t e i n theorem.

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Analytische Geometrie by Pickert G.


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