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We give a necessary and sufficient condition for the orientability of a locally standard 2-torus manifold with a fixed point which generalizes previous results of Nakayama-Nishimura in 2005 and Soprunova-Sottile in 2013. We construct…

The aim of this paper is to provide a proof for a version of Morse inequality for manifolds with boundary. Our main results are certainly known to the experts on Morse theory, nevertheless it seems necessary to write down a complete proof…

This paper gives an exposition of the authors' harmonic deformation theory for 3-dimensional hyperbolic cone-manifolds. We discuss topological applications to hyperbolic Dehn surgery as well as recent applications to Kleinian group theory.…

This is a review of the theoretical aspects of the supersymmetric extension of the Standard Model of particle physics, extracted from Chapter 87 of the 2026 Review of Particle Physics, F. Takahashi et al. (Particle Data Group), Int. J. Mod.…

Minor changes in the exposition and small corrections on the previous version.

In this note we document a gap in an argument in the above paper, and point to new work in the literature giving a complete proof of the main result.

This paper studies irregularity-type invariants of special C-pairs, or "geometric orbifolds" in the sense of Campana. Under mild assumptions on the singularities, we show that the augmented irregularity of a C-pair (X,D) is bounded by its…

We consider natural conformal invariants arising from the Gauss-Bonnet formulas on manifolds with boundary, and study conformal deformation problems associated to them. The key technique we used is to derive boundary C^2 estimates directly…

In this paper author was proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted…

This is a revised version of the preprint which has been available electronically for a while. The paper will now appear in J. Ramanujan Math. Soc.

This note explains an error in Proposition 5.1 of "Fibers of tropicalization," Math. Z. 262 (2009), no. 2, 301-311, discovered by W. Buczynska and F. Sottile, and fills the resulting gap in the proof of the paper's main theorem.

This paper has been withdrawn by the author due to serious flaws in certain proofs. For instance, the method used to construct certain automorphic representations is flawed.

Geometrization theorem, fibered case: Every three-manifold that fibers over the circle admits a geometric decomposition. Double limit theorem: for any sequence of quasi-Fuchsian groups whose controlling pair of conformal structures tends…

We correct one erroneous statement made in our recent paper "Medial axis and singularities".

We consider Legendrian links and tangles in $J^1S^1$ and $J^1[0,1]$ equipped with Morse complex families over a field $\mathbb{F}$ and classify them up to Legendrian cobordism. When the coefficient field is $\mathbb{F}_2$ this provides a…

This paper contains corrections to Madea, Rosenberg, Torres-Ardila, "The Geometry of Loop Spaces II: Characteristic Classes," Advances in Math. (287), 2016, 485-518. The main change is that results about $\pi_1({\rm Diff}(M))$ are replaced…

Shephard (Canad. J. Math. 26: 302-321, 1974) proved a decomposition theorem for zonotopes yielding a simple formula for their volume. In this note we prove a generalization of this theorem yielding similar formulas for their intrinsic…

In this paper, we give a comparison version of Pythagorean Theorem to judge the lower or upper bound of the curvature of Alexandrov spaces (including Riemannian manifolds).

We correct the proofs of the main theorems in our paper "Limit theorems for Betti numbers of random simplicial complexes".

We show that the principal results of the article "The metric dimension of graph with pendant edges" [Journal of Combinatorial Mathematics and Combinatorial Computing, 65 (2008) 139--145] do not hold. In this paper we correct the results…