Uniform stability of twisted constant scalar curvature K\"ahler metrics

Understand

We introduce a norm on the space of test configurations, which we call the minimum norm.

• We conjecture that uniform K-stability with respect to this norm is equivalent to the existence of a constant scalar curvature K\"ahler metric.
• This notion of uniform K-stability is analogous to coercivity of the Mabuchi functional.
• We characterise the triviality of test configurations, by showing that a test configuration has zero minimum norm if and only if it has zero $L^2$-norm, if and only if it is almost trivial.