8 citations · 18 across the 14 of their papers we have counts for
15 papers
Gradient estimates for a parabolic partial differential equation under the Ricci-Bourguignon flow
José 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 smoo…
Classification of gradient Yamabe soliton hypersurfaces of space forms
Willian Isao Tokura, Marcelo Bezerra Barboza
In this paper we investigate gradient Yamabe solitons, either steady or shrinking, that can be isometrically immersed into space forms as hypersurfaces that admit an upper bound on…
Rigidity results for Riemann solitons
Tokura Willian, Barboza Marcelo, Batista Elismar +1
In this paper we take a look at conditions that make a Riemann soliton trivial, compacity being one of them. We also show that the behaviour at infinity of the gradient field of a…
Invariant solutions of gradient -Yamabe solitons
W. Tokura, M. Barboza, E. Batista +1
The purpose of this paper is to study gradient -Yamabe solitons conformal to pseudo-Euclidean space. We characterize all such solitons invariant under the action of an -d…
Triviality results for quasi -Yamabe solitons
Willian Tokura, Elismar Batista, Priscila Kai
In this paper, we show that any compact quasi -Yamabe gradient solitons must have constant -curvature. Moreover, we provide a certain condition for a compact quasi -Ya…
Rigidity results for quotient almost Yamabe solitons
Marcelo Bezerra Barboza, Willian Isao Tokura, Elismar Dias Batista +1
In this paper we investigate the structure of certain solutions of the fully nonlinear Yamabe flow, which we call quotient almost Yamabe solitons because they extend quite naturall…
Immersion of gradient almost Yamabe solitons into warped product manifolds
W. Tokura, L. Adriano, E. Batista +1
The purpose of this article is to study the geometry of gradient almost Yamabe solitons immersed into warped product manifolds whose potential is given by the he…
Triviality results for compact k-Yamabe solitons
Willian Tokura, Elismar Batista
In this paper, we show that any compact gradient k-Yamabe soliton must have constant -curvature. Moreover, we provide a certain condition for a compact k-Yamabe soliton to be…
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,…
Properties of Complete Noncompact Warped Product Gradient Yamabe Solitons
Willian Isao Tokura, Levi Adriano, Romildo Pina +1
In this paper, we look for properties of gradient Yamabe solitons on top of warped product manifolds. Utilizing the maximum principle, we find lower bound estimates for both the po…
On Warped Product Gradient Yamabe Solitons
Willian Isao Tokura, Levi Adriano, Romildo Pina +1
The purpose of this article is to study gradient Yamabe soliton on warped product manifolds. First, we prove triviality results in the case of noncompact base with limited warping…
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…