activity
20112026
most citedRicci-mean curvature flows in gradient shrinking Ricci solitons

10 citations · 43 across the 19 of their papers we have counts for

collaborators

19 papers

math.DG2026

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…

math.DG2025

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…

math.DG2024

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…

math.AP2022

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…

math.DG2021★ 1 cited

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…

math.DG2021★ 5 cited

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…

math.DG2021★ 4 cited

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…

math.DG2021★ 2 cited

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…

math.DG2020★ 10 cited

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…

math.DG2019

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…

math.AP2017★ 1 cited

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…

math.DG2017

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…

math.DG2017

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…

math.DG2016

Examples of Ricci-mean curvature flows

Hikaru Yamamoto

Let be a projective bundle over with . In this paper, we show that lens…

math.DG2015

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.…

math.DG2015★ 10 cited

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…

math.DG2013

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…

math.DG2012★ 3 cited

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…

math.DG2011★ 7 cited

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…