10 citations · 43 across the 19 of their papers we have counts for
19 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…
A lower bound for the radius of Weinstein's Lagrangian tubular neighborhood
Hikaru Yamamoto
For an immersed Lagrangian submanifold in a Kähler manifold , there exists a symplectic local diffeomorphism from a tubular neighborhood of the image of the zero section…
A note on Huisken monotonicity-type formula for the mean curvature flow in a gradient shrinking extended Ricci soliton background
José 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-sim…
Solvability of a semilinear heat equation on Riemannian manifolds
Jin Takahashi, Hikaru Yamamoto
We study the solvability of the initial value problem for the semilinear heat equation in a Riemannian manifold with a nonnegative Radon measure on as init…
Infinite-time incompleteness of noncompact Yamabe flow
Jin 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 conv…
Mirror of volume functionals on manifolds with special holonomy
Kotaro Kawai, Hikaru Yamamoto
We can define the ``volume'' for Hermitian connections on a Hermitian complex line bundle over a Riemannian manifold , which can be considered to be the ``mirror'' of the st…
Deformation theory of deformed Donaldson-Thomas connections for -manifolds
Kotaro Kawai, Hikaru Yamamoto
A deformed Donaldson-Thomas connection for a manifold with a -structure, which we call a -dDT connection, is a Hermitian connection on a Hermitian lin…
The real Fourier-Mukai transform of Cayley cycles
Kotaro Kawai, Hikaru Yamamoto
The real Fourier-Mukai transform sends a section of a torus fibration to a connection over the total space of the dual torus fibration. By this method, Leung, Yau and Zaslow introd…
Deformation theory of deformed Hermitian Yang-Mills connections and deformed Donaldson-Thomas connections
Kotaro Kawai, Hikaru Yamamoto
A deformed Donaldson-Thomas (dDT) connection is a Hermitian connection of a Hermitian line bundle over a -manifold satisfying a certain nonlinear PDE. This is considered t…
An -regularity theorem for line bundle mean curvature flow
Xiaoli Han, Hikaru Yamamoto
In this paper, we study the line bundle mean curvature flow defined by Jacob and Yau. The line bundle mean curvature flow is a kind of parabolic flows to obtain deformed Hermitian…
Solutions with time-dependent singular sets for the heat equation with absorption
Jin Takahashi, Hikaru Yamamoto
We consider the heat equation with a superlinear absorption term in and study the existence and nonexistence of nonnegative solutions wit…
Special Lagrangian and deformed Hermitian Yang-Mills on tropical manifold
Hikaru Yamamoto
From string theory, the notion of deformed Hermitian Yang-Mills connections has been introduced by Mariño, Minasian, Moore and Strominger. After that, Leung, Yau and Zaslow proved…
Gauss maps of the Ricci-mean curvature flow
Naoyuki Koike, Hikaru Yamamoto
In this paper, we investigate the Gauss maps of a Ricci-mean curvature flow. A Ricci-mean curvature flow is a coupled equation of a mean curvature flow and a Ricci flow on the ambi…
Examples of Ricci-mean curvature flows
Hikaru Yamamoto
Let be a projective bundle over with . In this paper, we show that lens…
Lagrangian self-similar solutions in gradient shrinking Kähler-Ricci solitons
Hikaru Yamamoto
In this paper, we give a lower bound estimate for the diameter of a Lagrangian self-shrinker in a gradient shrinking Kähler-Ricci soliton as an analog of a result of A. Futaki, H.…
Ricci-mean curvature flows in gradient shrinking Ricci solitons
Hikaru Yamamoto
Huisken studied asymptotic behavior of a mean curvature flow in a Euclidean space when it develops a singularity of type I, and proved that its rescaled flow converges to a self-sh…
Weighted Hamiltonian stationary Lagrangian submanifolds and generalized Lagrangian mean curvature flows in toric almost Calabi-Yau manifolds
Hikaru Yamamoto
In this paper we generalize examples of Hamiltonian stationary Lagrangian submanifolds constructed by Lee and Wang in to toric almost Calabi-Yau manifolds. We constr…
Special Lagrangians and Lagrangian self-similar solutions in cones over toric Sasaki manifolds
Hikaru Yamamoto
We construct some examples of special Lagrangian submanifolds and Lagrangian self-similar solutions in almost Calabi-Yau cones over toric Sasaki manifolds. For example, for any int…
Self-similar solutions to the mean curvature flows on Riemannian cone manifolds and special Lagrangians on toric Calabi-Yau cones
Akito Futaki, Kota Hattori, Hikaru Yamamoto
The self-similar solutions to the mean curvature flows have been defined and studied on the Euclidean space. In this paper we initiate a general treatment of the self-similar solut…