2021
DOI: 10.1007/s00526-021-02013-6
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The Nirenberg problem on high dimensional half spheres: the effect of pinching conditions

Abstract: In this paper we study the Nirenberg problem on standard half spheres $$(\mathbb {S}^n_+,g), \, n \ge 5$$ ( S + n , g ) , n ≥ 5 … Show more

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Cited by 11 publications
(12 citation statements)
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“…Remark 1.1 We point out that the assumption that z is not a local maximum is necessary indeed one can prove that at local maxima of K 1 all blow ups are isolated simple. See [1]. Furthermore under the assumption that ∂K/∂ν ≤ 0 at critical point of K 1 , other than local maxima, the existence of non simple blow up can be ruled out.…”
Section: That Is Limmentioning
confidence: 99%
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“…Remark 1.1 We point out that the assumption that z is not a local maximum is necessary indeed one can prove that at local maxima of K 1 all blow ups are isolated simple. See [1]. Furthermore under the assumption that ∂K/∂ν ≤ 0 at critical point of K 1 , other than local maxima, the existence of non simple blow up can be ruled out.…”
Section: That Is Limmentioning
confidence: 99%
“…Furthermore under the assumption that ∂K/∂ν ≤ 0 at critical point of K 1 , other than local maxima, the existence of non simple blow up can be ruled out. See [1] Actually it turns out that the existence of solutions blowing at the same boundary point with the energy of m boundary bubbles, m ≥ 2 is related to the existence of critical points of the following Kirchhoff-Routh type function:…”
Section: That Is Limmentioning
confidence: 99%
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“…Lemma 3.8 There exists a bounded pseudogradient W 2 3 such that the following holds : There is a constant…”
Section: Nest We Definementioning
confidence: 99%