# On weakly m-convex sets

## TL;DR

This paper investigates properties of weakly m-convex sets, explores shadow-related problems, and provides a lower bound on the number of balls needed to cast a shadow at a point on a sphere in 3D space.

## Contribution

It introduces new properties of weakly m-convex sets, analyzes shadow problems, and establishes a lower estimate for the number of balls required to create a shadow in Euclidean space.

## Key findings

- Properties of weakly m-convex sets were characterized.
- Various shadow problems were analyzed.
- A lower bound for the number of balls needed to cast a shadow was derived.

## Abstract

There were obtained some properties of weakly m-convex sets. Various kinds of the problem of shadow were investigated. There was obtained the lower estimation for the number of balls that are necessary to create a shadow at the point of the sphere in three-dimensional Euclidean space

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Source: https://tomesphere.com/paper/1703.06785