ICTS:32635

Interpolation by zero mean curvature and constant mean curvature surfaces and related problems.

(2025). Interpolation by zero mean curvature and constant mean curvature surfaces and related problems.. SciVideos. https://scivideos.org/index.php/icts-tifr/32635

Interpolation by zero mean curvature and constant mean curvature surfaces and related problems.. SciVideos, Aug. 27, 2025, https://scivideos.org/index.php/icts-tifr/32635 

          @misc{ scivideos_ICTS:32635,
            doi = {},
            url = {https://scivideos.org/index.php/icts-tifr/32635},
            author = {},
            keywords = {},
            language = {en},
            title = {Interpolation by zero mean curvature and constant mean curvature surfaces and related problems.},
            publisher = {},
            year = {2025},
            month = {aug},
            note = {ICTS:32635 see, \url{https://scivideos.org/index.php/icts-tifr/32635}}
          }
Rukmini Dey
Talk numberICTS:32635
Source RepositoryICTS-TIFR

Abstract

We will talk of interpolation problems of two types.

First type of interpolation we talk of is that given two real analytic curves can one interpolate them with a minimal or maximal surface or a CMC surface? -- a version of Plateau's problem. For minimal surfaces this problem was solved by Douglas and Rado in great generality. We show that indeed, if the curves are "close" enough in a certain sense, then interpolation is possible. We will also talk of existence of a maximal surface containing a given real analytic curve and a special singularity, under certain conditions.

The second type of interpolation we will talk about is given a array of surfaces placed at some periodic intervals, can one interpolate them by a minimal/maximal surface, in the sense that the height functions of surfaces at these arrays sum up to a height function of a minimal/maximal surface.This work uses some Euler-Ramanujan identities.