Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the limit of spectral measures associated to a test configuration   We apply the integral formula of volumes to the family of graded linear
series constructed from any test configuration. This solves the conjecture
raised by Witt--Nystr\"{o}m so that the sequence of spectral measures for the
induced $\mathbb{C}^*$-action on the central fiber converges to the canonical
Duistermatt--Heckman measure defined by the associated weak geodesic ray. As a
consequence, we show that the algebraic $p$-norm of the test configuration
equals to the $L^p$-norm of tangent vectors. Using this result, We may give a
natural energy theoretic explanation for the lower bound estimate on the Calabi
functional by Donaldson and prove the analogous result for the
K\"{a}hler--Einstein metric.

24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin