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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
1
vote
1
answer
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Global orthogonal coordinates on the open unit ball II
Original question here:
Global orthogonal coordinates on the open unit ball
So let $v_i:\mathbb{R}\to\text{Im }v_i\subset\mathbb{R}$ be diffeomorphisms, $1\leq i\leq n$, $\mathbb{R}^n=\mathbb{R}^{n_1 …
3
votes
0
answers
95
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Tchebychev coordinates on hyperbolic space
Is there any known example of an open subset $U\subset\mathbb{H}^n$ with infinite volume admitting (global) Tchebychev coordinates for $n\geq3$?
6
votes
1
answer
235
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Global orthogonal coordinates on the open unit ball
Is there any diffeomorphism $x:\mathbb{R}^n\to\text{Im }x=B_1\left(0\right)\subset\mathbb{R}^n$ such that
$x$ is an orthogonal chart, i.e., the coordinate vector fields $X_i=\partial x/\partial u_i …