We construct a complete, embedded minimal surface in euclidean 3-space which has unbounded Gaussian curvature. It has infinite genus, infinitely many catenoidal type ends and one limit end.
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The study finds translators for higher order mean curvature flows in Euclidean and hyperbolic spaces.
problem Finding translators for higher order mean curvature flows in different spaces.
method Analyzing velocity functions of translators to -mean curvature flows in and .
result Existence and uniqueness of translators, including bowl-type, catenoid-type, and Grim Reaper-type translators.
In this paper we construct an example of a complete immersed minimal surface in of genus one with two embedded catenoid-type ends, one Enneper-type end and total Gauss curvature The proof of the existence of this example, was obtained using the Weierstrass representation, the theory of elliptic f…
The paper proves existence and classification of translating solitons in warped product manifolds.
problem Existence and classification of translating solitons in warped product manifolds.
method Proving existence and classification results for translating solitons defined as initial conditions for higher order mean curvature flows in warped product manifolds.
result Existence and classification of translating solitons in warped product manifolds.
The paper constructs surfaces with prescribed mean curvature in a specific space.
problem Finding surfaces with a given mean curvature in a particular geometric space.
method Phase plane analysis to construct entire rotational graphs and catenoid-type surfaces.
result Classification result for surfaces with linearly prescribed mean curvature.
Classifies and constructs translators for curvature flows.
problem Understanding translating solitons in curvature flows.
method Developed rotational theory, introduced signed-neck framework.
result Classified and constructed catenoidal-type translators.
In this short paper we extend the classical Hoffman-Meeks Halfspace Theorem to self-shrinkers, that is: "Let be a hyperplane passing through the origin. The only properly immersed self-shrinker contained in one of the closed half-space determined by is ." Our proof is geometric and uses a catenoid ty…
Minimal Lagrangian surfaces in complex hyperbolic quadric via loop group method.
problem Characterizing and constructing minimal Lagrangian surfaces in complex hyperbolic quadric.
method Loop of flat connections, isometric deformations, DPW-type representation.
result Explicit examples of minimal Lagrangian surfaces, including catenoid-type examples.
Researchers classify translators and rotators in hyperbolic 3-space for mean curvature flow.
problem Classifying translators and rotators in hyperbolic 3-space for mean curvature flow.
method Existence and uniqueness proofs, tangency principle application, classification of constant mean curvature translators and rotators.
result Existence and uniqueness of two distinct families of complete rotational translators in hyperbolic 3-space.