Multiplicity results for the scalar curvature problem on half spheres Article Swipe
Mohamed Ben Ayed
,
Khalil El Mehdi
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.3934/dcds.2024013
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.3934/dcds.2024013
Given a smooth positive function $ K $ defined on the standard half sphere endowed with its standard metric $ g $, we consider the problem of finding a metric $ \tilde{g} $ conformally equivalent to $ g $ and whose scalar curvature is equal to $ K $ and the boundary mean curvature is equal to zero. Using careful study of Hopf-Poincaré counting index formulae, we prove the existence of many of such metrics $ \tilde{g} $ provided that $ K $ is close to the scalar curvature of $ g $. Such Counting index formulae are related to the topological contribution of solutions at the level sets of the associated approximate variational functional. The location of the levels of these solutions are given very precisely which leads to a new type of multiplicity results on half spheres. Such multiplicity results are proved without any assumptions of symmetry or periodicity on the function $ K $.
Related Topics
Concepts
Scalar curvature
Multiplicity (mathematics)
SPHERES
Curvature
Mathematics
Prescribed scalar curvature problem
Mathematical analysis
Physics
Geometry
Classical mechanics
Sectional curvature
Astronomy
Metadata
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- article
- Language
- en
- Landing Page
- https://doi.org/10.3934/dcds.2024013
- OA Status
- diamond
- Cited By
- 1
- References
- 14
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4391997773
All OpenAlex metadata
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https://openalex.org/W4391997773Canonical identifier for this work in OpenAlex
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https://doi.org/10.3934/dcds.2024013Digital Object Identifier
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Multiplicity results for the scalar curvature problem on half spheresWork title
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articleOpenAlex work type
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enPrimary language
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2024Year of publication
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2024-01-01Full publication date if available
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Mohamed Ben Ayed, Khalil El MehdiList of authors in order
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https://doi.org/10.3934/dcds.2024013Publisher landing page
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YesWhether a free full text is available
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diamondOpen access status per OpenAlex
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https://doi.org/10.3934/dcds.2024013Direct OA link when available
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Scalar curvature, Multiplicity (mathematics), SPHERES, Curvature, Mathematics, Prescribed scalar curvature problem, Mathematical analysis, Physics, Geometry, Classical mechanics, Sectional curvature, AstronomyTop concepts (fields/topics) attached by OpenAlex
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1Total citation count in OpenAlex
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2024: 1Per-year citation counts (last 5 years)
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10Other works algorithmically related by OpenAlex
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