# A curvature flow approach to Lp-Christoffel-Minkowski problem for p>1

## TL;DR

This paper introduces a curvature flow method to address the Lp-Christoffel-Minkowski problem for p>1, providing a unified approach to solving this geometric problem involving convex hypersurfaces.

## Contribution

It develops a curvature flow technique to solve the Lp-Christoffel-Minkowski problem for p>1, advancing the understanding of convex hypersurface evolution.

## Key findings

- Established a curvature flow approach for p>1
- Provided convergence results for the flow
- Unified the solution framework for the Lp-Christoffel-Minkowski problem

## Abstract

We study the motion of smooth, closed, strictly convex hypersurfaces in Rn+1 expanding in the direction of their normal vector field with speed depending on the k-th elementary symmetric polynomial of the principal radii of curvature. As an application, we gives a unifed fow approach to Lp-Christoffel-Minkowski problem for p > 1.

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Source: https://tomesphere.com/paper/1907.03649