Finite area and volume of pointed $k$-surfaces

TL;DR

This paper introduces a concept of volume for pointed k-surfaces, demonstrating that both the volume and surface area are always finite, thus providing new insights into their geometric properties.

Contribution

The paper defines the volume of pointed k-surfaces and proves that both volume and surface area are finite, extending previous studies on these surfaces.

Findings

Volume of pointed k-surfaces is always finite.

Surface area of pointed k-surfaces is always finite.

Provides a new geometric measure for pointed k-surfaces.

Abstract

We define the ``volume'' contained by pointed $k$-surfaces, first studied by the author in [9], and we show that this volume is always finite. Likewise, we show that the surface area of a pointed $k$-surface is always finite.