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Results tagged with analytic-functions
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user 1441
22
votes
Is a function with nowhere vanishing derivatives analytic?
Yes, any such function is analytic.
Assume contrary, let $f$ be such a function.
Note that if it is analytic at two points then it has to be analytic everywhere between. So by taking restriction, we …
- 45k
22
votes
Accepted
Can a Riemannian metric be analytic in non-analytically different coordinates?
The answer is yes — the change of variables between is necessarily analytic.
The harmonic functions have to be analytic in both of your coordinates.
So you can pass from one of your coordinates to s …
- 45k