Related papers: Moon in a puddle and the four-vertex theorem

Free ribbon lemma that every free sphere-link in the 4-sphere is a ribbon sphere-link is shown in an earlier paper by the author. In this paper, another proof of this lemma is given.

We give a new proof of Lucas' Theorem in elementary number theory.

The uniform image of the full moon is well known from the beginning of history. In the last decades, there are photos with a similar configuration of the earth observed from the moon and from space, as well as of all the planets and their…

We expose here a short proof of Cramer's theorem in R based on convex duality.

In this paper, we proved the normal scalar curvature conjecture and the Bottcher-Wenzel conjecture.

We motivate and then prove a generalized pythagorean theorem for parallelepipeds in Euclidean space.

We begin with recalling the correspond theorem of induced modules and global sections of vector bundles. After that, we give a generalization of this theorem. Finally, we apply the result to branching laws, and give some concrete examples.

We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.

Beginning from the resolution of the Dirichlet L function, using the inner product formula between two infinite-dimensional vectors in the complex space, the author proved the baffling problem--Hecke conjecture.

We provide an elementary proof of a lemma that plays an important role in the classification of parallel mean curvature surfaces in two-dimensional complex space forms.

In this note we use the monodromy argument to prove a Noether-Lefschetz theorem for vector bundles.

We give a proof for the fundamental theorem of algebra,using the Fredholm index phenomena

In this paper, we prove a sharp convergence theorem for the mean curvature flow of arbitrary codimension in spheres which improves Baker's convergence theorem. In particular, we obtain a new differentiable sphere theorem for submanifolds in…

We prove a subadjunction theorem which relates the multi-adjoint linear system of the ambient space and the linear system of the restricted bundle on a subvariety.

We review our construction of the Teichm\"uller TQFT. We recall our volume conjecture for this TQFT and the examples for which this conjecture has been established. We end the paper with a brief review of our new formulation of the…

Standard proofs of Lusin's theorem, using simple functions, are sometimes quite elaborate. Here, we give a one-sentence proof of Lusin's theorem. We do not believe our approach, by way of inverse images, is new. However, this particular…

This paper proves a generalization of the Butterfly Theorem, a classical Euclidean result, which is valid in the complex projective plane.

This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.

Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.

We give a cycle-theoretic proof of the Gross-Zagier conjecture in weight four for several modular curves of genus zero.