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# Extreme values on restricted domains watch

1. Say I have a function f(v)=y of a vector v=(x_1, ..., x_n), whose domain is restricted by being bounded by x_1^2 + ... + x_n^2 =< r^2. (y is a real number).

Now, I'd like to investigate max/min values on the boundary of this n-dimensional sphere, what's a proper parametrization?

E.g. in the two-dimensional case it's appropriate to use x_1 = sqrt(r) cos t, x_2 = sqrt(r) sin t. But what if n>2?

Using rv/|v| is daunting at best.

Thanks.

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Updated: April 12, 2006
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