Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMinimal Surfaces in G2 Manifolds
134
0
0.0
(
0
)
Authors
Andrew Clarke
Ask ChatGPT about the research
No Arabic abstract
We consider immersions of a Riemann surface into a manifold with $G_2$-holonomy and give criteria for them to be conformal and harmonic, in terms of an associated Gauss map.
rate research
Read More
In this article we present an elementary introduction to the theory of minimal surfaces in Euclidean spaces $mathbb R^n$ for $nge 3$ by using only elementary calculus of functions of several variables at the level of a typical second-year undergraduate analysis course for students of Mathematics at European universities. No prior knowledge of differential geometry is assumed.
In this article, we interpolate a given real analytic spacelike curve $a$ in Lorentz-Minkowski space $mathbb{L}^3$ to another real analytic spacelike curve $c$, which is close enough to $a$ in a certain sense, by a maximal surface using inverse function theorem for Banach spaces. Using the same method we also interpolate a given real analytic curve $a$ in Euclidean space $mathbb{E}^3$ to another real analytic curve $c$, which is close enough to $a$ in a certain sense, by a minimal surface. The Bjorling problem and Schwartzs solution to it play an important role.
Let $a: Ito mathbb{R}^3 $ be a real analytic curve satisfying some conditions. In this article, we show that for any real analytic curve $l:Ito mathbb R^3$ close to $a$ (in a sense which is precisely defined in the paper) there exists a translation of $l$, and a minimal surface which contains both $ a $ and the translated $l$.
In this paper we consider the Matsumoto metric $F=frac{alpha^2}{alpha-beta}$, on the three dimensional real vector space and obtain the partial differential equations that characterize the minimal surfaces which are graphs of smooth functions and then we prove that plane is the only such surface. We also obtain the partial differential equation that characterizes the minimal translation surfaces and show that again plane is the only such surface.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
