# Smoothness in the $l_p$ Minkowski problem for $p<1$

## TL;DR

This paper investigates the regularity and convexity properties of solutions to the $L_p$ Minkowski problem for $p<1$, focusing on cases where the measure has a positive density, advancing understanding of geometric measure problems.

## Contribution

It provides new insights into the smoothness and strict convexity of solutions for the $L_p$ Minkowski problem when $p<1$, a less-explored parameter range.

## Key findings

- Solutions exhibit smoothness under positive density conditions.
- Strict convexity of solutions is established for $p<1$.
- Results extend the theory of the Minkowski problem to new parameter regimes.

## Abstract

We discuss the smoothness and strict convexity of the solution of the $L_p$ Minkowski problem when $p<1$ and the given measure has a positive density function.