MiS Preprint Repository
We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Floating bodies in neutral equilibrium
Robert Finn and Mattie SlossAbstract
In the paper just preceding in this issue, Finn proved that if the contact angle γ of a convex body B with a given liquid is π/2, and if B can be made to float in “neutral equilibrium” in the liquid in any orientation, then B is a metric ball. The present work extends that result, with an independent proof, to any contact angle in the range 0 < γ < π. Our result is equivalent to the general geometric theorem that if for every orientation of a plane, it can be translated to meet a given strictly convex body B in a fixed angle γ within the above range, then B is a metric ball.
- Received:
- 06.11.07
- Published:
- 06.11.07
- MSC Codes:
- 76B45, 52A15
- Keywords:
- capillarity, contact angle, floating criteria, convex bodies, neutral equilibrium