# Conformal Geometry and the Composite Membrane Problem

Analysis and Geometry in Metric Spaces (2013)

- Volume: 1, page 31-35
- ISSN: 2299-3274

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topSagun Chanillo. "Conformal Geometry and the Composite Membrane Problem." Analysis and Geometry in Metric Spaces 1 (2013): 31-35. <http://eudml.org/doc/266809>.

@article{SagunChanillo2013,

abstract = {We show that a certain eigenvalue minimization problem in two dimensions for the Laplace operator in conformal classes is equivalent to the composite membrane problem. We again establish such a link in higher dimensions for eigenvalue problems stemming from the critical GJMS operators. New free boundary problems of unstable type arise in higher dimensions linked to the critical GJMS operator. In dimension four, the critical GJMS operator is exactly the Paneitz operator.},

author = {Sagun Chanillo},

journal = {Analysis and Geometry in Metric Spaces},

keywords = {Eigenvalue Minimization in Conformal classes; GJMS operators; Composite Membrane problem; Free Boundary Problems; Conformal Geometry; Paneitz operator; eigenvalue minimization in conformal classes; composite membrane problem; free boundary problems; conformal geometry; paneitz operator},

language = {eng},

pages = {31-35},

title = {Conformal Geometry and the Composite Membrane Problem},

url = {http://eudml.org/doc/266809},

volume = {1},

year = {2013},

}

TY - JOUR

AU - Sagun Chanillo

TI - Conformal Geometry and the Composite Membrane Problem

JO - Analysis and Geometry in Metric Spaces

PY - 2013

VL - 1

SP - 31

EP - 35

AB - We show that a certain eigenvalue minimization problem in two dimensions for the Laplace operator in conformal classes is equivalent to the composite membrane problem. We again establish such a link in higher dimensions for eigenvalue problems stemming from the critical GJMS operators. New free boundary problems of unstable type arise in higher dimensions linked to the critical GJMS operator. In dimension four, the critical GJMS operator is exactly the Paneitz operator.

LA - eng

KW - Eigenvalue Minimization in Conformal classes; GJMS operators; Composite Membrane problem; Free Boundary Problems; Conformal Geometry; Paneitz operator; eigenvalue minimization in conformal classes; composite membrane problem; free boundary problems; conformal geometry; paneitz operator

UR - http://eudml.org/doc/266809

ER -

## References

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