4 citations · 7 across the 5 of their papers we have counts for
5 papers
On Warped Product Gradient Ricci-Harmonic Soliton
Elismar Batista, Levi Adriano, Willian Tokura
In this paper we study gradient Ricci-Harmonic soliton with structure of warped product manifold. We obtain some triviality results for the potential function, warping function and…
Static Perfect Fluids With Symmetries
Marcelo Barboza, Willian Tokura, Levi Adriano
In this paper we utilize symmetries in order to exhibit exact solutions to Einstein's equation of a perfect fluid on a static manifold all of whose spatial factor belongs to the co…
Gradient Estimates on Warped Product Gradient Almost Ricci Solitons
Willian Isao Tokura, Levi Adriano, Romildo Pina +1
In this paper, by slightly modifying Li-Yau's technique so that we can handle drifting Laplacians, we were able to find three different gradient estimates for the warping function,…
On Warped Product Gradient Yamabe Soliton
Willian I. Tokura, Levi Adriano, Romildo Pina
In this paper, we provide a necessary and sufficient conditions for the warped product to be a gradient Yamabe soliton when the base is conformal to an n-dimensiona…
The Caffarelli-Kohn-Nirenberg Inequalities on Metric Measure Spaces
Willian Isao Tokura, Levi Adriano, Changyu Xia
In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Caffarelli-Kohn-Nirenberg inequality with same exponent n(n>1), then it has e…