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

We prove some injectivity theorems. Our proof depends on the theory of mixed Hodge structures on cohomology groups with compact support. Our injectivity theorems would play crucial roles in the minimal model theory for higher-dimensional…

We consider the Lane-Emden conjecture which states that there is no non-trivial non-negative solution for the Lane-Emden system whenever the pair of exponents is subcritical. By Sobolev embeddings on $S^{N-1}$ and scale invariance of the…

In this research article, we formulate and prove multidimensional Widder--Arendt theorem and integrated form of multidimensional Widder--Arendt theorem for functions with values in sequentially complete locally convex spaces. Established…

In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.

In this paper, making use of Theorem 2 of [5], we establish a new four critical points theorem which can be regarded as a companion to Theorem 1 of [4]. We also present an application to the Dirichlet problem for a class of quasilinear…

We prove a vanishing theorem for the twisted de Rham cohomology of a compact manifold.

A mid-point theorem is proved in an elementary way for the U type shape of functions that arise out of exponential quadratic functions. These results are inspired from epidemic patterns and growth over a time period. Key words: natural…

A strong form of the Manin-Peyre conjecture with a power saving error term is proved for a certain cubic fourfold.

In this paper we study the inversion in an ellipse and some properties, which generalizes the classical inversion with respect to a circle. We also study the inversion in an ellipse of lines, ellipses and other curves. Finally, we…

We introduce an algebra given by quadratic relations in an algebra of polynomials in an infinite number of variables. Using this algebra, we prove some explicit formulas for the Sturm sequence of a polynomial.

We use the square peg problem for smooth curves to prove a generalized table Theorem for real valued functions on Riemannian surfaces with odd Euler characteristic. We then use this result to prove the table conjecture for even functions on…

In this paper, we give a simple proof of the Gauss-Bonnet-Chern theorem for a real oriented Finsler vector bundle with rank equal to the dimension of the base manifold. As an application, a Gauss-Bonnet-Chern formula for any…

In this oaper, we prove some fixed point theorems in metric vector spaces, in which the continuity is not required for the considered mappings to satisfy. We provide some concrete examples to demonstrate these theorems. We also give some…

We give a new proof of the butterfly theorem, based on the use of several expressions involving the scale factor between the two wings.

In this paper, we shall prove the Chung-Feller Theorem in several ways. We provide an inductive proof, bijective proof, and proofs using generating functions, and the Cycle Lemma of Dvoretzky and Motzkin.

We introduce a supporting combinatorial framework for the Flat Wall Theorem. In particular, we suggest two variants of the theorem and we introduce a new, more versatile, concept of wall homogeneity as well as the notion of regularity in…

In this paper we present another proof of the analytic version of the Hahn-Banach theorem in terms of convex functionals.

We prove a combination theorem for PD(n)-pairs.

Beginning from the resolution of Dirichlet L function, using the inner product formula of infinite-dimensional vectors in the complex space, the author proved the world's baffling problem--Generalized Riemann hypothesis.

We give a one-sentence proof of McLaughlin and Rundell's inverse uniqueness theorem.