Submanifold Geometry, Lie Group Action and Its Applications to Theoretical Physics 2026

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Registration information will be announced later.

• Jaigyoung Choe (Korea Institute for Advanced Study (KIAS), Korea)
• Keomkyo Seo (Sookmyung Women's University, Korea)
• Kurando Baba (Tokyo University of Science, University of Augsburg): online
• Naotoshi Fujihara (Tokyo University of Science)
• Shota Hamanaka (University of Tsukuba)
• Kotaro Kawai (Beijing Institute of Mathematical Sciences and Applications, China)
• Isami Koga (Kyushu International University)
• Reiko Miyaoka (Tohoku University)
• Shinji Ohno (Nihon University)
• Jun Sasaki (Institute of Science Tokyo)
• Makiko Sumi Tanaka (Tokyo University of Science)
• Yuta Yamauchi (Yokohama National University)

November 21 (Saturday)

• 9:57 - 10:00 Opening Ceremony
• 10:00 - 11:00 Keomkyo Seo (Sookmyung Women's University, Korea)
• 11:15 - 12:15 Makiko Sumi Tanaka (Tokyo University of Science)

Photo and Lunch

• 14:10 - 15:10 Naotoshi Fujihara (Tokyo University of Science)
• 15:20 - 16:20 Shota Hamanaka (University of Tsukuba)
• 16:35 - 17:35 Kurando Baba (Tokyo University of Science & University of Augsburg): Online talk

November 22 (Sunday)

• 9:50 - 10:50 Jaigyoung Choe (Korea Institute for Advanced Study (KIAS), Korea)
• 11:00 - 12:00 Reiko Miyaoka (Tohoku University)

Lunch

• 13:50 - 14:50 Yuta Yamauchi (Yokohama National University)
• 15:00 - 16:00 Kotaro Kawai (Beijing Institute of Mathematical Sciences and Applications, China)
• 16:15 - 17:15 Shinji Ohno (Nihon University)

Banquet (18:30-, Namba)

November 23 (Monday)

• 10:00 - 11:00 Jun Sasaki (Institute of Science Tokyo)
• 11:10 - 12:10 Isami Koga (Kyushu International University)

Photo

Jaigyoung Choe (Korea Institute for Advanced Study (KIAS), Korea)
Title: Reflection principle across a sphere for free boundary minimal surfaces
Abstract: A Schwarz-type reflection principle is established for a minimal surface meeting a sphere orthogonally along its free boundary. The reflection is obtained under some condition on the principal curvature of the minimal surface along the boundary. As an application, we consider an embedded free boundary minimal annulus A in a ball. Suppose that the Taylor series of the principal curvature of A along its free boundary has infinite radius of convergence. Then A must be the critical catenoid.

Keomkyo Seo (Sookmyung Women's University, Korea)
Title: Rigidity Results for Steklov-Type Problems on Riemannian Manifolds
Abstract: We study sharp lower bounds for first eigenvalues of Steklov-type problems on compact Riemannian surfaces with smooth boundary. Under natural lower curvature assumptions on the Gaussian curvature of the surface and the geodesic curvature of the boundary, we obtain optimal eigenvalue estimates and characterize the equality case by the Euclidean disk. We also consider Serrin-type overdetermined boundary value problems related to Steklov eigenvalues. We present symmetry and rigidity results for overdetermined Steklov problems on domains in Riemannian manifolds with nonnegative Ricci curvature.

Kurando Baba (Tokyo University of Science, University of Augsburg): online
Title: Equifocal Hypersurfaces in Symmetric Spaces of Compact Type and Backward Mean Curvature Flows
Abstract: Liu-Terng (2009, 2020) gave an explicit analysis of the mean curvature flow starting from isoparametric submanifolds in spheres, in both the forward and backward directions of time. After them, their theory has been extended to equifocal submanifolds in symmetric spaces of compact type: the forward direction by Koike (2011), and the backward direction by Liu-Radeschi (2022), who proved the existence of long-time solutions of the backward mean curvature flow. However, the asymptotic analysis of these long-time solutions, carried out by Liu-Terng for isoparametric hypersurfaces, has not been available in this setting. In this talk, we extend this analysis to equifocal hypersurfaces in symmetric spaces of compact type. First, we show that the mean curvature and the squared norm of the shape operator of an equifocal hypersurface are expressed in terms of the tangential focal data. Next, by using these formulas, we explicitly describe the exponential decay of the mean curvature and the limit of the squared norm of the shape operator along the long-time solution of the backward mean curvature flow, and estimate their ratio. Finally, based on these results, we propose an extension of the conjectures of Liu-Terng to symmetric spaces of compact type. This talk is based on joint work with Naoyuki Koike (Tokyo University of Science).
[2607.25025] Equifocal hypersurfaces in symmetric spaces of compact type and backward mean curvature flows

Naotoshi Fujihara (Tokyo University of Science)
Title: Weighted curve shortening flow in orbifolds and cohomogeneity-one Lagrangian mean curvature flow
Abstract: Under the curve shortening flow (CSF), an embedded closed curve in a closed surface either shrinks to a point in finite time or exists for all time. If it exists for all time, its geodesic curvature converges to zero and the curve approaches a geodesic. In this talk, we prove that similar results hold for the weighted CSF in a compact 2-dimensional orbifold with finitely many cone points. Moreover, we present the correspondence between the weighted CSF and cohomogeneity-one Lagrangian mean curvature flow (LMCF) under suitable assumptions, and the graphical convergence of the LMCF to a minimal Lagrangian submanifold. This talk is based on joint work with Toru Kajigaya (Shibaura Institute of Technology) and Albert Wood (King's College London).

Shota Hamanaka (University of Tsukuba)
Title: Weighted Yamabe flow and weighted ADM mass
Abstract: I'll discuss weighted Yamabe flows on asymptotically flat smooth metric measure spaces and its interaction with the weighted ADM mass. I'll first show that the asymptotically flat structure is preserved along the flow. Under an appropriate assumption, I'll show that the weighted ADM mass is constant and that the weighted Einstein--Hilbert functional is non-increasing provided that the initial weighted scalar curvature is nonnegative. Under another weaker assumption, I'll show instead that the weighted ADM mass is monotone non-increasing along the flow. If time permits, I'll also present some results about long-time existence and convergence of the flow and the mass. The content of this talk is based on the joint work with Pak Tung Ho (Tamkang University) and Jinwoo Shin (Sookmyung Women's University).

Kotaro Kawai (Beijing Institute of Mathematical Sciences and Applications, China)
Title: Anisotropic calibration
Abstract: In this talk, I will introduce anisotropic calibration, which is a generalization of calibration by Harvey and Lawson. An interesting example appears when a manifold admits a calibration and a calibrated distribution. Then an anisotropic calibration can be obtained by taking a certain type of (formal) adiabatic limit. There is a similar correspondence in the connection side via the Fourier-Mukai transform which gives the "mirror" correspondence. This talk is based on joint work with Tommaso Pacini (University of Turin).

Isami Koga (Kyushu International University)
Title: TBA

Shinji Ohno (Nihon University)
Title: On the Intersection of Two Real Flag Manifolds in Complex Flag Manifolds
Abstract: A complex flag manifold is obtained as an orbit of the adjoint action of a compact semisimple Lie group, which is a compact, simply connected, homogeneous Kähler manifold. A connected component of the fixed-point set of an anti-holomorphic involutive isometry on a Kähler manifold is called a real form. Real forms provide examples of totally geodesic Lagrangian submanifolds and have been studied from various viewpoints. In this talk, we discuss the intersection of two real flag manifolds that arise as real forms of a complex flag manifold. We provide necessary and sufficient conditions for the intersection to be discrete in greater detail than previously known, and show that such a discrete intersection can be obtained as an orbit of a certain Weyl group. Finally, we present an example where the involutions defining the two real flag manifolds cannot be made to commute. This talk is based on joint work with Osamu Ikawa (Kyoto Institute of Technology) and Kurando Baba (Tokyo University of Science).

Reiko Miyaoka (Tohoku University)
Title: Chern's conjecture in the Dupin case [PDF]
Abstract: Chern's conjecture (1968) states that a closed minimal hypersurface $M^n$ in $S^{n+1}$ is isoparametric if the scalar curvature is constant (CSC). For $g = \#\{\lambda_1, \dots, \lambda_n\}$, the first non-trivial case $g=3$ was solved affirmatively. Isoparametric hypersurfaces have $g\in \{1,2,3,4,6\}$, and the cases $g=4,6$ are extremely intricate. Under the additional assumption that $M$ is a proper Dupin, i.e., $\lambda_i$ and its multiplicity are constant along its curvature distribution, we show: $M$ is isoparametric if (1) $g=3$, (2) $g=4$, and CSC or CLC, (3) $g=6$ and CLC [JMSJ, in press]. Here, CLC means constant Lie curvature, i.e., the cross ratio of distinct four principal curvatures is constant. This quantity is introduced by the author (1989) as an invariant under Lie contact transformations.

Jun Sasaki (Institute of Science Tokyo)
Title: On Higgs triples and Higgs quadruplets
Abstract: Let $E, F$ be smooth complex vector bundles over a compact Riemann surface $M$. A Higgs triple $(D_E^{\prime\prime}, D_F^{\prime\prime}, \varphi)$ consists of structures of Higgs bundles $D_E^{\prime\prime}$ in $E$ and $D_F^{\prime\prime}$ in $F$ and a morphism $\varphi: (F, D_F^{\prime\prime})\to (E, D_E^{\prime\prime})$. A Higgs quadruplet $(D_E^{\prime\prime}, D_F^{\prime\prime}, \varphi, \psi)$ consists of a Higgs triple $(D_E^{\prime\prime}, D_F^{\prime\prime}, \varphi)$ and a morphism $\psi: (E, D_E^{\prime\prime})\to (F, D_F^{\prime\prime})$ satisfying that $\varphi\circ\psi=\psi\circ\varphi=0$. Higgs triples can be considered as generalizations of holomorphic triples introduced by Garc\’{i}a-Prada and one can introduce the notion of $\tau$-stability for Higgs triples, depending on a real number $\tau$. Higgs triples and Higgs quadruplets were introduced by Takashi Ono in 2025. Garc\’{i}a-Prada introduced holomorphic triples via a dimensional reduction of $SU(2)$-equivariant holomorphic vector bundles over $M\times\mathbb{CP}^1$. In a similar way, Ono introduced Higgs quadruplets via a dimensional reduction of $SU(2)$-equivariant Higgs bundles over $M\times\mathbb{CP}^1$ and introduced the notion of $\tau$-stability for Higgs quadruplets, depending on a real number $\tau$. On the other hand, Higgs triples have not been obtained through such a dimensional reduction. In this talk, we prove that under a suitable assumption, if a Higgs quadruplet $(D_E^{\prime\prime}, D_F^{\prime\prime}, \varphi, \psi)$ is stable, then $\psi=0$ holds. From this, it follows that stable Higgs triples can be obtained via a dimensional reduction of $SU(2)$-equivariant Higgs bundles over $M\times\mathbb{CP}^1$. Moreover, we prove that the moduli space of stable Higgs triples is a non-singular complex manifold.

Makiko Sumi Tanaka (Tokyo University of Science)
Title: Geometry of oriented Lagrangian Grassmann manifolds
Abstract: The oriented Lagrangian Grassmann manifold $U(n)/SO(n)$, consisting of all oriented Lagrangian subspaces of $\mathbb C^n$, is a double covering of the Lagrangian Grassmann manifold $U(n)/O(n)$ and is a compact Riemannian symmetric space. B. Y. Chen and T. Nagano introduced the notions of polars, meridians, centrioles, and antipodal sets for compact Riemannian symmetric spaces. All of these notions are defined in terms of geodesic symmetries. Polars, meridians, and centrioles are totally geodesic submanifolds, while antipodal sets are finite subsets, and these objects play an important role in understanding the global geometry of compact Riemannian symmetric spaces. Although these objects have been determined for many compact Riemannian symmetric spaces, they have not yet been described for oriented Lagrangian Grassmann manifolds. In this talk, we give explicit descriptions of the polars, meridians, centrioles, and maximal antipodal sets of oriented Lagrangian Grassmann manifolds. This talk is based on joint work with Hiroyuki Tasaki.

Yuta Yamauchi (Yokohama National University)
Title: Minimal total absolute curvature for equiaffine immersions
Abstract: For immersions of compact n-dimensional manifolds into Euclidean space, the total absolute curvature is a global geometric quantity defined by integrating the absolute value of the Lipschitz–Killing curvature. The Chern–Lashof theorem states that the total absolute curvature is bounded below by the sum of the Betti numbers. Moreover, it is equal to 2 if and only if the image is a convex hypersurface embedded in an (n+1)-dimensional affine subspace. In 2001, Koike introduced the total absolute curvature for equiaffine immersions of arbitrary dimension and codimension, and established a Chern–Lashof type inequality. However, a geometric characterization of the case in which the total absolute curvature attains its minimum value had remained unknown in the equiaffine setting. In this talk, we investigate the relationship between the minimality of the total absolute curvature and convexity for equiaffine immersions, without assuming the non-degeneracy of the affine fundamental form. We prove that the total absolute curvature is equal to 2 if and only if the image is a convex hypersurface embedded in an (n+1)-dimensional affine subspace.