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Grant support

S. Cruz and G. Vaira have been supported by INdAM - GNAMPA Project 2022 "Fenomeni di blow-up per equazioni non lineari", E55F22000270001S and by PRIN 2017JPCAPN.

Analysis of institutional authors

Cruz-Blazquez, SergioAuthor

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January 14, 2025
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POSITIVE BLOW-UP SOLUTIONS FOR A LINEARLY PERTURBED BOUNDARY YAMABE PROBLEM

Publicated to:DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - 2024-12-24 (), DOI: 10.3934/dcds.2024174

Authors: Cruz-blazquez, Sergio; Vaira, Giusi

Affiliations

Univ Bari, Bari, Italy - Author

Abstract

We consider the problem of prescribing the scalar and boundary mean curvatures via conformal deformation of the metric on a n - dimensional compact Riemannian manifold. We deal with the case of negative scalar curvature K and boundary mean curvature H of arbitrary sign which are non - constant and D-n = root n( n - 1)H |K|(- 1/2) > 1 at some point of the boundary. It is known that this problem admits a positive mountain pass solution if n = 3, while no existence results are known for n >= 4. We will consider a perturbation of the geometric problem and show the existence of a positive solution which blows-up at a boundary point which is critical for both prescribed curvatures.

Keywords

Blow-up solutionCompactnessConformal metricConformal metricsConstant mean-curvatureDeformatioExistence theoremManifoldsPrescribed curvature problemScalar-flat metrics

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2024 there are still no calculated indicators, but in 2023, it was in position 163/332, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics, Applied.

Impact and social visibility

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Italy.

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (CRUZ BLAZQUEZ, SERGIO) .