https://neckpinch.com/authors/kin-ming-hui/New arXiv papers by Kin Ming Hui, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2107.13685/arxiv:2107.13685Thu, 29 Jul 2021 00:00:00 GMTKin Ming Hui — By using fixed point argument we give a proof for the existence of singular rotationally symmetric steady and expanding gradient Ricci solitons in higher dimensions with metric g=(da²)/(h(a²))+a²g_(Sⁿ) for some function h where g_(Sⁿ) is the standard metric on the unit sphere Sⁿ in ℝⁿ for any n≥ 2. More precisely for any λ≥ 0 and c₀>0, we prove that there exist infinitely many solutions h∈ C²((0,∞);ℝ⁺) for the equation 2r²h(r)hᵣᵣ(r)=(n-1)h(r)(h(r)−1)+rhᵣ(r)(rhᵣ(r)−λr-(n-1)), h(r)>0, in (0,∞) satisfying undersetsubstackr→ 0lim r^(√n-1)h(r)=c₀ and prove the higher order asymptotic behaviour of the global singular solutions near the origin. We also find conditions for the existence of unique global singular solution of such equation in terms of its asymptotic behaviour near the origin.Ricci solitonsRotational symmetry & warped products