Abstract.
We explore some geometric aspects of compensation compactness associated to Jacobian determinants. We provide the optimal constant in Wente's inequality - the original motivation of this work - and go on to give various extensions to geometric situations. In fact we improve Wente's inequality somewhat, making it more appropriate for applications in which optimal results are required. This is demonstrated when we prove an optimal inequality for immersed surfaces of constant mean curvature in \( \Bbb {R}^3 \), contolling their diameter in terms of their area and curvature.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Author information
Authors and Affiliations
Additional information
Received: November 4, 1996
Rights and permissions
About this article
Cite this article
Topping, P. The optimal constant in Wente's $ L^\infty $ estimate. Comment. Math. Helv. 72, 316–328 (1997). https://doi.org/10.1007/s000140050018
Published:
Issue Date:
DOI: https://doi.org/10.1007/s000140050018