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Results tagged with asymptotics
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user 138705
Asymptotic behavior of functions, asymptotic series and related topics
6
votes
0
answers
120
views
Given the Ricci decays rapidly to 0 at infinity, is the metric asymptotically flat?
In terms of those coordinates, does $f$ enjoy the same asymptotics that it does enjoy in the usual spherical coordinates $(r,\theta,\phi)$? What is the relation between both coordinates? …
- 969
2
votes
2
answers
157
views
Asymptotic Behaviour of Solutions to a Riccati-type ODE with Small Forcing Term
Consider the following ODE:
$$f'(r) = f^2(r) + O \left( \frac{1}{r^4} \right)$$
as $r$ goes to infinity. The initial conditions are $f(1) = C <0$.
What is the behaviour of a solution $f$ at infinity …
- 969
3
votes
1
answer
162
views
$\Delta_g f = 0$ on the Riemannian Manifold $(\mathbb{R}^3 \setminus B , g)$ with conditions...
I think if g is the euclidean metric, the asymptotics are:
$$f = 1+ \frac{C}{r} + O \left( \frac{1}{r^{2}} \right)$$
where $C$ is some constant and $r=\sqrt{x^2+y^2+z^2}$ in cartesian coordinates. …
- 969