Shijie Gu

activity

20132026

most citedContractible open manifolds which embed in no compact, locally connected and locally 1-connected metric space

4 citations · 7 across the 15 of their papers we have counts for

collaborators

16 papers

math.MG2026

The disjoint disks property for Busemann $G$ -spaces

Tadashi Fujioka, Shijie Gu

We prove that every finite-dimensional Busemann $G$-space of dimension at least five has the disjoint disks property (DDP). For a sufficiently small metric sphere $L=S(c,r)$, w…

math.GT2026

Kwasik--Schultz manifolds are $Z$ -compactifiable

Shijie Gu

Kwasik and Schultz constructed two-ended open $4$ -manifolds which satisfy the usual finiteness and stability conditions at infinity but do not admit arbitrarily small $1$ -neighborh…

math.MG2026

Busemann G-spaces with convex balls

Tadashi Fujioka, Shijie Gu

We prove that any Busemann G-space such that every sufficiently small metric ball is convex is a topological manifold. The key ingredient in the proof is Ivanov's Helly theorem. Th…

math.DG2026

Finsler structure of Busemann G-spaces

Tadashi Fujioka, Shijie Gu

We provide two sufficient conditions for a Busemann G-space to admit a differentiable DC atlas with a continuous Finsler metric, from the viewpoint of comparison geometry. These re…

math.GT2025

Nonembeddable contractible open manifolds arising from Whitehead doubling

Shijie Gu, Jian Wang, Yanqing Zou

We study a family of genus-one contractible open manifolds constructed by iterated Whitehead doubling from a nontrivial knot $K$ and an even half-twist $m$ . For each such pair, we…

math.DG2025

Topological regularity of Busemann spaces of nonpositive curvature

Tadashi Fujioka, Shijie Gu

We extend the topological results of Lytchak-Nagano and Lytchak-Nagano-Stadler for CAT(0) spaces to the setting of Busemann spaces of nonpositive curvature, i.e., BNPC spaces. We g…

math.GT2023

On Z-compactifiability of manifolds

Shijie Gu

In 1976, Chapman and Siebenmann established necessary and sufficient conditions for $Z$ -compactifying Hilbert cube manifolds. Although the corresponding conditions are known to be…

math.GT2020

$Z$ -compactifiable manifolds which are not pseudo-collarable

Shijie Gu

It is shown that there exist $Z$ -compactifiable manifolds with noncompact boundary which fail to be pseudo-collarable.

math.GT2018★ 4 cited

Contractible open manifolds which embed in no compact, locally connected and locally 1-connected metric space

Shijie Gu

This paper pays a visit to a famous contractible open 3-manifold $W^{3}$ proposed by R. H. Bing in 1950's. By the finiteness theorem \cite{Hak68}, Haken proved that $W^{3}$ can embed i…

math.GT2018★ 1 cited

Characterization of pseudo-collarable manifolds with boundary

Shijie Gu

In this paper we obtain a complete characterization of pseudo-collarable $n$ -manifolds for $n \geq 6$ . This extends earlier work by Guilbault and Tinsley to allow for manifolds with…

math.GT2017

Compactifications of manifolds with boundary

Shijie Gu, Craig R. Guilbault

This paper is concerned with "nice" compactifications of manifolds. Siebenmann's iconic dissertation characterized open manifolds M^m (m>5) compactifiable by addition of a manifold…

math.GT2014

A hierarchy for closed n-cell-complements

Robert J. Daverman, Shijie Gu

Let $C$ and $D$ be a pair of crumpled $n$ -cubes and $h$ a homeomorphism of $Bd C$ to $Bd D$ for which there exists a map $f_{h} : C \to D$ such that $f_{h} ∣ Bd C = h$ …

math.AP2013

A Study of Weakly Discontinuous Solutions for Hyperbolic Differential Equations Based on Wavelet Transform Methods

Shijie Gu

A new approach to prove the one-dimensional Cauchy problem's weakly discontinuous solutions for hyperbolic PDEs are on the characteristics is discussed in this paper. To do so, I u…

math.GT2013★ 2 cited

On the Shrinkable U.S.C. Decomposition Spaces of Spheres

Shijie Gu

Let $G$ be a u.s.c decomposition of $S^{n}$ , $H_{G}$ denote the set of nondegenerate elements and $π$ be the projection of $S^{n}$ onto $S^{n} / G$ . Suppose that each point in the decomposit…

math.AP2013

A Study of Weakly Discontinuous Solutions for Hyperbolic Differential Equations Based on Wavelet Transform Methods

Shijie Gu

A new way to prove the one-dimensional Cauchy problem's weakly discontinuous solutions for hyperbolic PDEs are on the characteristics is discussed in this paper. To do so, I use wa…

math.GT2013

Shrinkability of Decomposition of $S^{n}$ Having Arbitrarily Small Neighborhoods with ( $n - 1$ )-Sphere Frontiers

Shijie Gu

Let $G$ be a usc decomposition of $S^{n}$ , $H_{G}$ denote the set of nondegenerate elements and $π$ be the natural projection of $S^{n}$ onto $S^{n} / G$ . Suppose that each point in the deco…

The disjoint disks property for Busemann G-spaces

Kwasik--Schultz manifolds are Z-compactifiable

Busemann G-spaces with convex balls

Finsler structure of Busemann G-spaces

Nonembeddable contractible open manifolds arising from Whitehead doubling

Topological regularity of Busemann spaces of nonpositive curvature

On Z-compactifiability of manifolds

Z-compactifiable manifolds which are not pseudo-collarable

Contractible open manifolds which embed in no compact, locally connected and locally 1-connected metric space

Characterization of pseudo-collarable manifolds with boundary

Compactifications of manifolds with boundary

A hierarchy for closed n-cell-complements

A Study of Weakly Discontinuous Solutions for Hyperbolic Differential Equations Based on Wavelet Transform Methods

On the Shrinkable U.S.C. Decomposition Spaces of Spheres

A Study of Weakly Discontinuous Solutions for Hyperbolic Differential Equations Based on Wavelet Transform Methods

Shrinkability of Decomposition of Sn Having Arbitrarily Small Neighborhoods with (n−1)-Sphere Frontiers

The disjoint disks property for Busemann $G$ -spaces

Kwasik--Schultz manifolds are $Z$ -compactifiable

$Z$ -compactifiable manifolds which are not pseudo-collarable

Shrinkability of Decomposition of $S^{n}$ Having Arbitrarily Small Neighborhoods with ( $n - 1$ )-Sphere Frontiers