MathOverflow

Are there any non-Einstein Kähler metric in dimension $4$ with maximal volume growth? If assumed Einstein, they have to be Ricci flat and hence classified by Kronheimer's hyperKähler ones and their quotients.

Let $X$ be an infinite-dimensional complex Banach space, and let $\mathcal{B}(X)$ denote the algebra of all bounded linear operators on $X$. For $T \in \mathcal{B}(X)$, write $\sigma(T)$ for its spectrum.
It is known that the commutant of a nilpotent operator on an infinite-dimensional space contains a compact operator with infinite spectrum. A standard proof can be found in: M. Oudghiri, K. Souilah, Generalized Drazin inverse and commuting Riesz perturbations...

One difference between morphisms in abstract category theory and concrete functions between sets lies in the way they handle function composition.
For sets $A,B,C,D$ and functions $f\colon A \to B$ and $g\colon C \to D$, the composition$g\circ f$ is always defined if the image satisfies $f[A] \subseteq C$. Even in the case that $B \nsubseteq C$. Whereas in category theory on a basic level there...

(Much edited with new details, contour plot, and tags.)
We wish to solve the 5th power system,
$$x_1^k + x_2^k + x_3^k = y_1^k + y_2^k + y_3^k$$