Consider a conformal mapping (whose domain and codomain may be either subsets of $\mathbb{R}^n$ or of $\mathbb{C}^n$).
- I wonder if it is always differentiable over its domain?
- Is it always partially differentiable over its domain?
My questions comes from the following quote from Wikipedia, which seems assume the answers to the above questions true:
The conformal property may be described in terms of the Jacobian derivative matrix of a coordinate transformation. If the Jacobian matrix of the transformation is everywhere a scalar times a rotation matrix, then the transformation is conformal.
Thanks and regards!