Spheres can be stretched to have larger diameter than antipodal distance.
problem Finding the maximum diameter of spheres relative to antipodal points.
method Deformation of spheres in dimensions ≥3.
result Spheres can be deformed to have diameter larger than antipodal distance.
Y. Nikonorov completes a proof in a geometry paper.
problem Completing a proof in a geometry paper.
method Completing an argument from a previous proof.
result Proof of Theorem 2.5 in JGA 27 (2017) is now complete.
We show how one can handle the formalism developped by Yurii Vorobjev in order to give general results about the problems of linearisation and of normal form of a Poisson structure in the neighborhood of one of its symplectic leaves.
This is an English translation of the following paper, published several years ago: Nikonorov Yu.G. On the geodesic diameter of surfaces with involutive isometry (Russian), Tr. Rubtsovsk. Ind. Inst., 2001, V. 9, 62-65, Zbl. 1015.53041. All inserted footnotes provide additional information related to the mentioned probl…
Research characterizes critical points of scalar curvature functionals.
problem Characterizing critical points of scalar curvature functionals.
method Translation and analysis of a previous Russian paper.
result Provides insights into critical points of scalar curvature functionals.
The paper studies stability of Einstein metrics on non-simple Lie group homogeneous spaces.
problem Classifying compact homogeneous spaces with standard Einstein metrics.
method Analysis of scalar curvature functional and coindex.
result Most standard Einstein metrics on non-simple Lie group homogeneous spaces are unstable.
Study Einstein Lie groups and geodesic orbit manifolds, finding some are not geodesic orbit.
problem Characterizing Einstein Lie groups and geodesic orbit manifolds.
method Characterizing GimesK-invariant geodesic orbit metrics on Lie groups G for regular subgroups K. result Extensive classes of compact simple Einstein Lie groups are not geodesic orbit manifolds.
Normalized Ricci flow preserves positivity of Ricci curvature on some generalized Wallach spaces.
problem Preserving positivity of Ricci curvature on generalized Wallach spaces.
method Normalized Ricci flow analysis on generalized Wallach spaces.
result Normalized Ricci flow does not preserve positivity of Ricci curvature on certain generalized Wallach spaces.
New algorithms optimize faster for simpler problems in machine learning.
problem Design faster optimization algorithms for practical machine learning problems.
method Adaptive gradient algorithms with refined conditions based on Hessian singular values.
result Achieved optimal gradient complexity for linear regression.