# The Hessian of quantized Ding functionals and its asymptotic behavior

## TL;DR

This paper analyzes the Hessian of quantized Ding functionals, proving their convexity along Bergman geodesics and exploring their asymptotic behavior through Berezin-Toeplitz quantization, advancing understanding in Kähler geometry.

## Contribution

It provides an elementary proof of convexity for quantized Ding functionals and investigates their asymptotic properties using Berezin-Toeplitz quantization.

## Key findings

- Convexity of quantized Ding functionals along Bergman geodesics established.
- Asymptotic behavior of the Hessian characterized via Berezin-Toeplitz quantization.
- Elementary proof technique simplifies understanding of the functional's convexity.

## Abstract

We compute the Hessian of quantized Ding functionals and give an elementary proof for the convexity of quantized Ding functionals along Bergman geodesics from the view point of projective geometry. We study also the asymptotic behavior of the Hessian using the Berezin-Toeplitz quantization.