Distance geometry in Riemannian manifolds-with-boundary

F. J. Almgren, Jr., Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints, Memoirs A. M. S. #165, A. M. S., Providence, 1976.
MATH Google Scholar
Ralph Alexander and S. Alexander, Geodesics in Riemannian manifolds-with-boundary, preprint.
Google Scholar
I. D. Berg, An estimate on the total curvature of a geodesic in Euclidean 3-space-with-boundary, preprint.
Google Scholar
H. Busemann, The geometry of geodesics, Academic Press, New York, 1955.
MATH Google Scholar
M. P. do Carmo and F. W. Warner, Rigidity and convexity of hypersurfaces in spheres, J. Differential Geometry 4(1970), 133–144.
MathSciNet MATH Google Scholar
T. Hasegawa, The index theorem of geodesics on a Riemannian manifold with boundary, Kodai Math. J. 1(1978), 285–288.
Article MathSciNet MATH Google Scholar
F.-E. Wolter, Interior metric, shortest paths and loops in Riemannian manifolds with not necessarily smooth boundary, Diplomarbeit, Technische Universität Berlin.
Google Scholar
F.-E. Wolter, Shortest paths and loops, distance function and cut-loci in Riemannian manifolds with boundary, research announcement.
Google Scholar
W. Rinow, Die Innere Geometrie der Metrischen Räume, Springer, Berlin, 1961.
Book MATH Google Scholar
R. Sacksteder, On hypersurfaces with no negative sectional curvatures, Amer. J. Math. 82(1960), 609–630.
Article MathSciNet MATH Google Scholar

Download references

Author information

Authors and Affiliations

University of Illinois, 61801, Urbana, Illinois, U.S.A.
S. Alexander

Authors

S. Alexander
View author publications
You can also search for this author in PubMed Google Scholar

Editor information

Dirk Ferus Wolfgang Kühnel Udo Simon Bernd Wegner

Rights and permissions

Reprints and permissions

Copyright information

About this paper

Cite this paper

Alexander, S. (1981). Distance geometry in Riemannian manifolds-with-boundary. In: Ferus, D., Kühnel, W., Simon, U., Wegner, B. (eds) Global Differential Geometry and Global Analysis. Lecture Notes in Mathematics, vol 838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088837

Download citation

DOI: https://doi.org/10.1007/BFb0088837
Published: 03 October 2006
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10285-4
Online ISBN: 978-3-540-38419-9
eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Distance geometry in Riemannian manifolds-with-boundary

Access this chapter

Preview

References