# Bounded $H_\infty$-calculus for cone differential operators

## TL;DR

This paper establishes that certain cone differential operators possess a bounded $H_$-calculus, enabling advanced analysis of PDEs like the Laplacian and porous medium equation on manifolds with conical singularities.

## Contribution

It proves the bounded $H_$-calculus for parameter-elliptic cone differential operators, extending analytical tools for PDEs on singular manifolds.

## Key findings

- Bounded $H_$-calculus established for cone differential operators.
- Applications to Laplacian and porous medium equation on warped conical manifolds.
- Enhanced analytical framework for PDEs on singular geometric spaces.

## Abstract

We prove that parameter-elliptic extensions of cone differential operators have a bounded $H_\infty$-calculus. Applications concern the Laplacian and the porous medium equation on manifolds with warped conical singularities.