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We study the balanced resistance forms on the Julia sets of Misiurewicz-Sierpinski maps, which are self-similar resistance forms with equal weights. In particular, we use a theorem of Sabot to prove the existence and uniqueness of balanced…

Functional Analysis · Mathematics 2020-08-19 Shiping Cao , Malte S. Hassler , Hua Qiu , Ely Sandine , Robert S. Strichartz

Recently ,mathematicians have been interested in studying the theory of discrete dynamical system, specifically difference equation, such that considerable works about discussing the behavior properties of its solutions (boundedness and…

Dynamical Systems · Mathematics 2025-12-25 Zeraoulia Rafik , A. H. Salas

We extend the well-known Sacks-Uhlenbeck energy gap result (1981) for harmonic maps from closed Riemann surfaces into closed Riemannian manifolds from the case of maps with small energy (thus near a constant map), to the case of harmonic…

Analysis of PDEs · Mathematics 2019-09-23 Paul M. N. Feehan

We utilize a three-dimensional manifold to solve Riemann Problems that arise from a system of two conservation laws with quadratic flux functions. Points in this manifold represent potential shock waves, hence its name wave manifold. This…

We prove a generalisation of Elkies' theorem to nonunimodular definite forms (and lattices). Combined with inequalities of Froyshov and of Ozsvath and Szabo, this gives a simple test of whether a rational homology 3-sphere may bound a…

Geometric Topology · Mathematics 2008-02-12 Brendan Owens , Saso Strle

We present a number of rigidity results concerning holomorphic dynamical systems admitting rotation quasicircles. Firstly, we show the absence of line fields on the Julia set of any rational map that is geometrically finite away from a…

Dynamical Systems · Mathematics 2025-09-05 Willie Rush Lim

We extend harmonic map techniques to the setting of more general differential equations in conformal geometry. We obtain an extension of Siu's rigidity to Kahler-Weyl geometry and apply the latter to Vaisman's conjecture. Other applications…

Differential Geometry · Mathematics 2014-02-26 Gerasim Kokarev

On any metric space, I provide an intrinsic characterization of those complex-valued functions which are uniform limits of Lipschitz functions. There are applications to function theory on complete Riemannian manifolds and, in particular,…

Functional Analysis · Mathematics 2021-05-18 L. A. Coburn

In a previous paper, we constructed an explicit dynamical correspondence between certain Kleinian reflection groups and certain anti-holomorphic rational maps on the Riemann sphere. In this paper, we show that their deformation spaces share…

Dynamical Systems · Mathematics 2023-01-23 Russell Lodge , Yusheng Luo , Sabyasachi Mukherjee

The Seiberg-Witten equations that have recently found important applications for four-dimensional geometry are the Euler-Lagrange equations for a functional involving a connection $A$ on a line bundle $L$ and a section $\phi$ of another…

dg-ga · Mathematics 2008-02-03 Juergen Jost , Xiaowei Peng , Guofang Wang

Equivalence classes of $n$-point configurations in Euclidean, Hermitian, and quaternionic spaces are related, respectively, to classical determinantal varieties of symmetric, general, and skew-symmetric bilinear forms. Cayley-Menger…

Algebraic Geometry · Mathematics 2007-05-23 Ciprian S. Borcea

Among the nondegenerate C^4 hypersurfaces M in R^n, we characterize the rational quadrics as the hypersurfaces that are the least well approximated by rational points. Given M other than a rational quadric, we prove a heuristically sharp…

Number Theory · Mathematics 2025-12-02 Alexander Smith

The relative equilibria of a symmetric Hamiltonian dynamical system are the critical points of the so-called augmented Hamiltonian. The underlying geometric structure of the system is used to decompose the critical point equations and…

Differential Geometry · Mathematics 2007-05-23 Pascal Chossat , Debra Lewis , Juan-Pablo Ortega , Tudor S. Ratiu

We prove an infinite-dimensional generalization of Zenger's lemma that was used in the proof of the fact that the convex hull of the point spectrum of a linear operator is contained in its numerical range. Two relevant examples are given,…

Functional Analysis · Mathematics 2016-08-14 Roman Drnovšek

In this paper we provide extensions of the $\lambda$-Lemma (also known as Inclination Lemma) for piecewise smooth vector fields and maps. In order to achieve our main result, we investigate the regularity of time-T-maps of piecewise smooth…

Dynamical Systems · Mathematics 2025-07-16 Claudio A. Buzzi , Paulo Santana , Luan V. M. F. Silva

We use the methods developed with M. Lyubich for proving complex bounds for real quadratics to extend E. De Faria's complex a priori bounds to all critical circle maps with an irrational rotation number. The contracting property for…

Dynamical Systems · Mathematics 2016-09-06 Michael Yampolsky

We prove several relations between spectrum and dynamics including wave trace expansion, sharp/improved Weyl laws, propagation of singularities and quantum ergodicity for the sub-Riemannian (sR) Laplacian in the four dimensional…

Differential Geometry · Mathematics 2019-09-04 Nikhil Savale

We construct a Poisson map between manifolds with linear Poisson brackets corresponding to the two samples of Lie algebra $e(3)$. Using this map we establish equivalence of the Steklov-Lyapunov system and the motion of a particle on the…

Exactly Solvable and Integrable Systems · Physics 2015-06-26 A. V. Tsiganov

Zakalyukin's lemma asserts that the coincidence of the images of two wave front germs implies the right equivalence of corresponding map germs under a certain genericity assumption. The purpose of this paper is to give an improvement of…

Differential Geometry · Mathematics 2021-09-14 Atsufumi Honda , Kosuke Naokawa , Kentaro Saji , Masaaki Umehara , Kotaro Yamada

Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction…

Mathematical Physics · Physics 2011-09-13 Manuel Calixto , Julio Guerrero , Juan Carlos Sánchez-Monreal
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