https://neckpinch.com/authors/hikaru-yamamoto/New arXiv papers by Hikaru Yamamoto, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2604.14366arxiv:2604.14366Wed, 15 Apr 2026 00:00:00 GMTJosé N. V. Gomes, Willian I. Tokura, Hikaru Yamamoto — We study the Ricci-Bourguignon flow on warped product manifolds with noncompact base. This setting leads naturally to a parabolic partial differential equation on the space of smooth warping functions, arising from the necessary and sufficient conditions for a warped metric to evolve under the flow. One of our main results establishes a gradient estimate for this equation, providing the analytic input for the geometric applications developed herein and, in particular, recovering classical gradient estimates for the heat equation under the Ricci flow. Furthermore, we develop a method for constructing explicit warped product solutions to the Ricci-Bourguignon flow and present examples that illustrate the scope and geometric relevance of our resultsRicci flowBoundaries & non-compactRotational symmetry & warped products https://arxiv.org/abs/2412.19939arxiv:2412.19939Fri, 27 Dec 2024 00:00:00 GMTJosé N. V. Gomes, Matheus Hudson, Hikaru Yamamoto — We give an application of a Huisken monotonicity-type formula for the mean curvature flow in a compact smooth manifold with a Riemannian metric that evolves by a shrinking self-similar solution of the extended Ricci flow. Our investigation builds on previous articles by Huisken and the third author, as we apply their techniques to establish new results in this geometric setting. Moreover, under some natural geometric assumptions, the noncompact case is also solvedRicci flowMean curvature flowRicci solitonsBoundaries & non-compact https://arxiv.org/abs/2111.03222arxiv:2111.03222Fri, 05 Nov 2021 00:00:00 GMTJin Takahashi, Hikaru Yamamoto — We show the noninheritance of the completeness of the noncompact Yamabe flow. Our main theorem states the existence of a long time solution which is complete for each time and converges to an incomplete Riemannian metric. This shows the occurrence of the infinite-time incompleteness.Yamabe flowSingularitiesBoundaries & non-compactLong-time existence & convergence