Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

2 results

  • Minimal arcs in metric spaces

  • S. K. Hildebrand, Harold Willis Milnes
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics / Volume 19 / Issue 4 / June 1975
    Published online by Cambridge University Press:
    09 April 2009, pp. 426-430
    Print publication:
    June 1975
    • Article
      • You have access
    • PDF
    • Export citation

  • In this paper we discuss the existence of an are of minimal length joining two arbitrary, yet fixed points in a complete metric space, where the metric is restricted only by the properties (A) and (B) given below. It is shown that under these conditions an arc of least length joining any two fixed points exists, and is unique. In addition, its length is shown to be equal to the metrie distance between the points.

  • A technique for finding minimal paths in subspaces of a metric space

  • Harold Willis Milnes, S. K. Hildebrand
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics / Volume 19 / Issue 3 / May 1975
    Published online by Cambridge University Press:
    09 April 2009, pp. 312-320
    Print publication:
    May 1975
    • Article
      • You have access
    • PDF
    • Export citation

  • In this paper the problem of constructing an arc of minimum length joining two fixed points: P1, P2, in an arbitrary subset: S, of a metric space is considered. The approach taken is a departure from the classical methods of the calculus of variations in that it is topological character, making use of the properties of sets rather than differential calculus.