Brakke flow
Regularity theory in geometric measure theory
Elliptic and parabolic partial differential equations
Kotaro Motegi, Non-uniqueness of Brakke flows starting from minimal surfaces with singularities, preprint, arXiv:2608.13531.
Kotaro Motegi, L2 normal velocity implies strong solution for graphical Brakke flows, Advances in Calculus of Variations, vol. 19, no. 4, 2026, pp. 689-698.
Oct 1, 2026 Second-order regularity of Brakke flows with a forcing term, The Second Workshop on Geometric Variational Problems, Geometric Measure Theory, and Related Topics, Oral presentation, Academia Sinica.
Sep 14, 2026 Second-order regularity of Brakke flows, MATRIX-RIMS Tandem-workshop: Geometric flows and related phenomena, Oral presentation, Kyoto Univarsity.
Sep 3, 2026 Dynamical instability of minimal surfaces, MSJ Autumn Meeting 2026, Oral presentation, Kobe University.
Jun 30, 2026 Second-order regularity theorem for weak mean curvature flow, European School of Differential Geometry 2026, Poster presentation, Università degli Studi dell'Aquila.
Mar 23, 2026 A regularity theorem for weak solutions to mean curvature flow with forcing term, MSJ Spring Meeting 2026, Oral presentation, Tokyo University of Science.
Feb 16, 2026 Second-order regularity theorem for weak mean curvature flow, The 27th Northeastern Symposium on Mathematical Analysis, Poster presentation, Hokkaido University.
Sep 18, 2025 A regularity theorem for integral varifolds close to triple junction, MSJ Autumn Meeting 2025, Oral presentation, Nagoya University.
Feb 17, 2025 A regularity theorem for integral varifolds close to a triple junction, The 26th Northeastern Symposium on Mathematical Analysis, Poster presentation, Tohoku University.