In Part I of this article we generalize the Linearized Doubling (LD) approach, introduced in
earlier work by NK, by proving a general theorem stating that if $\Sigma $ is a closed …

Through desingularization of Clifford torus, we prove the existence of a sequence of
nondegenerate (in the sense of Duyckaerts–Kenig–Merle ([8])) nodal nonradial solutions to …

In this article, we survey recent progress on the variational theory related to mean curvature.
We will discuss the Morse theory of minimal hypersurfaces with an emphasis on the …

We prove the existence of branched immersed constant mean curvature (CMC) 2‐spheres
in an arbitrary Riemannian 3‐sphere for almost every prescribed mean curvature, and …

We demonstrate the existence of branched immersed 2-spheres with prescribed mean
curvature, with controlled Morse index and with arbitrary codimensions in closed …

For each large enough $ m\in\mathbb {N} $ we construct by PDE gluing methods a closed
embedded minimal hypersurface ${\breve {M} _m} $ doubling the equatorial three-sphere …

In this article, we construct complete embedded constant mean curvature surfaces in $\mb
{R}^ 3$ with freely prescribed genus and any number of ends greater than or equal to four …

In this article, we solve the constant mean curvature dirichlet problem on catenoidal necks
with small scale in $\mb {R}^ 3$. The solutions are found in exponentially weighted H\" older …

Conservation Laws and Gluing Constructions for Constant Mean Curvature (Hyper)Surfaces
Page 1 Conservation Laws and Gluing Constructions for Constant Mean Curvature (Hyper)Surfaces …

The authors study rotational hypersurfaces with constant Gauss-Kronecker curvature in ℝ n.
They solve the ODE associated with the generating curve of such hypersurface using …