这是一份kcl伦敦大学学院 5CCM223A作业代写的成功案
问题 1.
so we get
$$
H=\frac{1}{2}\left(\frac{\dot{g}}{f}-\frac{\ddot{f}}{\dot{g}}\right)
$$
Since $\dot{g}^{2}=1-\dot{f}^{2}, \mathcal{S}$ is minimal if and only if
$$
f \ddot{f}=1-\dot{f}^{2} .
$$
证明 .
To solve the differential equation (8), put $h=\dot{f}$, and note that
$$
\ddot{f}=\frac{d h}{d t}=\frac{d h}{d f} \frac{d f}{d t}=h \frac{d h}{d f} .
$$
Hence, Eq. (8) becomes
$$
f h \frac{d h}{d f}=1-h^{2}
$$
5CCM223A COURSE NOTES ：
$$
\iint_{\mathcal{S}} K d \mathcal{A}=0 \text {. }
$$
Can such a surface have $K=0$ everywhere?
Show that, if $\mathcal{S}$ is the ellipsoid
$$
\frac{x^{2}+y^{2}}{a^{2}}+\frac{z^{2}}{b^{2}}=1,
$$
where $a$ and $b$ are positive constants,
$$
\iint_{\mathcal{S}} K d \mathcal{A}=4 \pi \text {. }
$$