The study classifies and normalizes 3D gl-regular Nijenhuis operators.
problem Classifying and normalizing 3D gl-regular Nijenhuis operators.
method Classification and normal form proof.
result Proved A. Bolsinov's conjecture.
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Unique asymptotics found for special geometric flows.
problem Classifying ancient ovals of Ricci flow.
method Analyzing invariant, compact, non-self-similar solutions.
result Uniqueness of the profile function .
Study CMC hypersurfaces in with a specific symmetry.
problem Constant mean curvature hypersurfaces with double horocyclic symmetry in .
method Reduction to a single ODE, solving explicitly, classifying solutions.
result Existence and uniqueness of double horocyclic CMC hypersurfaces.
The paper classifies surfaces in the Heisenberg space invariant under specific isometries.
problem Classifying surfaces in the Heisenberg space with specific geometric properties.
method Analyzing surfaces with mean curvature under left-translations, rotations, and helicoidal motions.
result Classification of -translators invariant under specific isometries.
The paper classifies homogeneous hypersurfaces in three 4D Thurston geometries.
problem Classifying homogeneous hypersurfaces in specific 4D geometries.
method Analyzing isometry groups and applying classification techniques.
result Homogeneous hypersurfaces identified in , and .
Classification of homogeneous almost complex 4-manifolds with non-degenerate torsion bundle
problem Classification of homogeneous almost complex 4-manifolds with non-degenerate torsion bundle
method Classification using rigidity of structures
result Complete classification in the homogeneous setting