Abstract A. Fraser and R. Schoen proved the existence of free boundary minimal surfaces Σ
_n Σ n in B^ 3 B 3 which have genus 0 and n boundary components, for all n ≥ 3 n≥ 3. For …

In the Euclidean unit three-ball, we construct compact, embedded, two-sided free boundary
minimal surfaces with connected boundary and prescribed high genus, by a gluing …

This survey paper investigates, from a purely geometric point of view, Daniel's isometric
conjugation between minimal and constant mean curvature surfaces immersed in …

We construct a new family of entire solutions to the Yamabe equation− Δ u= n (n− 2) 4| u| 4
n− 2 u in D 1, 2 (R n). If n= 3 our solutions have maximal rank, being the first example in odd …

We develop an equivariant min-max theory as proposed by Pitts-Rubinstein in 1988 and
then show that it can produce many of the known minimal surfaces in $\mathbb {S}^ 3$ up to …

We construct a new family of high genus examples of free boundary minimal surfaces in the
Euclidean unit 3-ball by desingularizing the intersection of a coaxial pair of a critical …

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 …

In this paper we show for every sufficiently large integer $ g $ the existence of a complete
family of closed and embedded constant mean curvature (CMC) surfaces deforming the …

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 …

The Lawson surface ξ 1, g of genus g is constructed by rotating and reflecting the Plateau
solution ft with respect to a particular geodesic 4-gon Γ t across its boundary, where (t= 1 2 …