Question on minimal surfaces, or surfaces that have zero mean curvature.

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7
votes
1answer
265 views

why the K3 surfaces are minimal surfaces

I need to prove that all K3 surfaces are minimal surfaces, so that every birational map between K3 surfaces is an isomorphism. I've started to read beauville's book on complex algebraic surfaces: ...
0
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0answers
24 views

zero mean curvature and a variational problem

given the lagrangian $$ J(u)= \int_{V} \sqrt{1+|gra(u)|^{2})} $$ with the constraint $ \int_{V}udx =1 $ why is the volumen constraint there ? for teh case of R^{3} i know this must satisfy the ...
0
votes
1answer
220 views

compute principal directions of a cylinder

I calculated the parametric equation of a cylinder, $$x(u,v)=a\cos(u)$$ $$y(u,v)=a\sin(u)$$ $$z(u,v)=v$$ I do not know how to calculate principal directions ? I am not sure what it means neither ...