14 citations · 28 across the 21 of their papers we have counts for
22 papers · 1 filter
Multi-Module Minimal Products: Exact Composition, Closed Profiles, and Gaussian Transfer
Yongsheng Zhang
We establish an exact composition principle for spherical immersions coupled through coefficient profiles and norm-preserving bilinear maps. Under an explicit mixed-orthogonality c…
The Geometry and Dynamics of Spiral Minimal Products
Haizhong Li, Yongsheng Zhang
We study the spiral product , which couples two spherical -totally real immersed factors through a profile curve $γ=(z_1,z_2)\su…
Cones over minimal products cannot be calibrated by smooth calibrations
Yongsheng Zhang
We extend a key result in [Zha26], by establishing the obstruction that the minimal product structure (for minimal submanifolds or stationary currents in spheres) automatically mak…
Detect duality obstruction of calibrations in smooth category
Yongsheng Zhang
This paper consists of three parts: (a) exhibit a new gluing result which can dramatically simplify extensions of calibration pairs; (b) observe that every Lawlor cone can support…
Verifying spiral minimal product structure through the Takahashi Theorem
Yongsheng Zhang
We verify the spiral minimal product structure through the Takahashi Theorem with full computational details which were omitted in [LZ].
Some configuration results for area-minimizing cones
Yongsheng Zhang
We discover some very general configuration results for constructing area-minimizing cones. In particular, given any closed minimal submanifold in some Euclidean sphere, every cone…
Remarks on "Spiral Minimal Products"
Haizhong Li, Yongsheng Zhang
This note aims to give a better understanding and some remarks about recent preprint ``Spiral Minimal Products". In particular, 1. it should be pointed out that a generalized Delau…
Delaunay hypersurfaces in spheres
Yongsheng Zhang
We study Delaunay hypersurfaces in with and add a missing (flower) type of the category. Moreover, embedded Delaunay hypersurfaces of nonzero constant mean…
Spiral Minimal Products
Haizhong Li, Yongsheng Zhang
This paper exhibits a structural strategy to produce new minimal submanifolds in spheres based on two given ones. The method is to spin the given minimal submanifolds by a curve $γ…
Symmetry of hypersurfaces with symmetric boundary
Hui Ma, Chao Qian, Jing Wu +1
Let be a compact connected subgroup of . In , we gain interior -symmetry for minimal hypersurfaces and hypersurfaces of constant mean curvature (C…
On instability of Type (II) Lawson-Osserman Cones
Zhaohu Nie, Yongsheng Zhang
We obtain the instability of Type (II) Lawson-Osserman cones in Euclidean spaces, and thus provide a family of (uncountably many) unstable solutions with singularity to the Dirichl…
Recent progress on the Dirichlet problem for the minimal surface system and minimal cones
Yongsheng Zhang
This is a very brief report on recent developments on the Dirichlet problem for the minimal surface system and minimal cones in Euclidean spaces. We shall mainly focus on two direc…
Dirichlet boundary values on Euclidean balls with infinitely many solutions for the minimal surface system
Xiaowei Xu, Ling Yang, Yongsheng Zhang
We make systematic developments on Lawson-Osserman constructions relating to the Dirichlet problem (over unit disks) for minimal surfaces of high codimension in their 1977 Acta pap…
On the non-existence of solutions of the Dirichlet problem for the minimal surface system
Yongsheng Zhang
In this paper we study the non-existence of solutions to the Dirichlet problem for minimal graphs of codimension , including certain situations over domain even with no…
Minimizing cones associated with isoparametric foliations
Zizhou Tang, Yongsheng Zhang
Associated with isoparametric foliations of unit spheres, there are two classes of minimal surfaces minimal isoparametric hypersurfaces and focal submanifolds. By virtue of the…
New area-minimizing Lawson-Osserman cones
Xiaowei Xu, Ling Yang, Yongsheng Zhang
It has been 40 years since Lawson and Osserman introduced the three minimal cones associated with Dirichlet problems in their 1977 Acta paper [LO77]. The first cone was shown area-…
On Lawson-Osserman Constructions
Xiaowei Xu, Ling Yang, Yongsheng Zhang
Lawson-Osserman constructed three types of non-parametric minimal cones of high codimensions based on Hopf maps between spheres, which correspond to Lipschitz but non-differentiabl…
On extending calibration pairs
Yongsheng Zhang
The paper studies how to extend local calibration pairs to global ones in various situations. As a result, new discoveries involving mass-minimizing properties are exhibited. In pa…
On realization of tangent cones of homologically area-minimizing compact singular submanifolds
Yongsheng Zhang
We show that every area-minimizing hypercone and every oriented Lawlor cone in [Law91] can be realized as a tangent cone at a point of some homologically area-minimizing singular c…
On Extending Calibrations
Yongsheng Zhang
This is a companion note of [Zhaa] (arXiv:1501.01836) where the extension of local calibration pairs of smooth submanifolds is discussed. Here we emphasize on the case of singular…
How to construct metrics to control distributions of homologically mass-minimizing currents
Yongsheng Zhang
By Federer and Fleming there exist at least one mass-minimizing normal current in every real-valued homology class of a Riemannian manifold. However the regularity of the mass-mini…
On Lawson's area-minimizing hypercones
Yongsheng Zhang
We show the area-minimality property of all homogeneous area-minimizing hypercones in Euclidean spaces (classified by Lawlor) following Lawson's original idea in his 72' Trans. A.M…