数学试题讲解

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Let

Σ \subset R^{3}

be an embedded surface in

R^{3}

. A surface is calle

d

minimal if, for any

p \in Σ

, we have

κ_{1} (p) + κ_{2} (p) = 0

, whe re

κ_{1} (p)

and

κ_{2} (p)

are the two principal curvatures at

p

. Prov e that if

Σ

is closed, then

Σ

cannot be minimal.