= J JJ 2 V<f) l V<f, l dzdxdt ~2£ I Vltt dxdt 

 ° D l ° S Fo 



T T 



hj j h^ dxdt -J J (V 7 * 2 ) *2n d8dt 

 OS s T > / 



(12) 



where S_ is the projection of S„ on z = 0. When we take the variation of J, we have 

 Fo r J F 



= -J J J V 2 ^ dzdxdt -J j 6^ U ln+ i 



° D l ° S lFo V 



ltt 



dxdt 



S \ 



), 6 n /h +1 -h 1 dxdt 

 1 In x t 



"j j <W 6 *2n dzdt " j j 

 S T OS 



( *ln + *2n )6 *l dzdt 

 J 



Here, in addition to Equation (10) , the following equation holds 



J j +l*ltt dxdt * j j 6 *l*ltt dxdt + J j *l 6 *ltt 

 ° S Fo ° S Fo ° S Fo 



dxdt 



(12a) 



T T 



" 2 j J *>l+ltt dxdt + J ^l^lt^lt^t^-c dx = 2 \ \ 6 *i*itt 



° S Fo S Fo ° S Fo 



dxdt 



(13) 



