Related papers: On Pompeiu's-Schiffer's Conjectures from Shape Opt…
In this paper we describe a general strategy for approaching the Weinstein conjecture in dimension three. We apply this approach to prove the Weinstein conjecture for a new class of contact manifolds (planar contact manifolds). We also…
By making use of the classification of real simple Lie algebra, we get the maximum of the squared length of restricted roots case by case, thus we get the upper bounds of sectional curvature for irreducible Riemannian symmetric spaces of…
The Swampland Distance Conjecture postulates the emergence of an infinite tower of massless states when approaching infinite-distance points in moduli space. However, most string backgrounds are supported by fluxes, and therefore depart…
For any ring we propose the construction of a cover which increases the finitistic dimension on one side and decreases the finitistic dimension to zero on the opposite side. This complements recent work of Cummings.
We study degenerate quasilinear elliptic equations on Riemannian manifolds and obtain several Liouville theorems. Notably, we provide rigorous proof asserting the nonexistence of positive solutions to the subcritical Lane-Emden-Fowler…
Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve…
In this article, we present the theoretical basis for an approach to Stein's method for probability distributions on Riemannian manifolds. Using a semigroup representation for the solution to the Stein equation, we use tools from stochastic…
In this paper, we improve the finiteness constant for the finiteness principles for $C^m(\mathbb{R}^n,\mathbb{R}^d)$ and $C^{m-1,1}(\mathbb{R}^n,\mathbb{R}^D)$ selection proven by Fefferman, Israel, and the second author and extend the more…
The purpose of this paper is to give some new Diophantine applications of modularity results. We use the Shimura-Taniyama conjecture to prove effective finiteness results for integral points on moduli schemes of elliptic curves. For several…
This study revisits the problem of identifying the unknown interior Robin boundary of a connected domain using Cauchy data from the exterior region of a harmonic function. It investigates two shape optimization reformulations employing…
In this paper we investigate a problem of approximation of continuous mappings by smooth mappings with nonnegative Jacobian.
Optimized, necessary and sufficient conditions for the identification of the Schmidt number will be derived in terms of general Hermitian operators. These conditions apply to arbitrary mixed quantum states. The optimization procedure…
Numerical continuation in the context of optimization can be used to mitigate convergence issues due to a poor initial guess. In this work, we extend this idea to Riemannian optimization problems, that is, the minimization of a target…
This letter aims at resolving the issues raised in the recent short communication [1] and answered by [2] by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique…
In supersymmetric quantum mechanics, exact-solvability of one-dimensional quantum systems can be classified only with an additional assumption of integrability, the so-called shape invariance condition. In this paper we show that in the…
We study approximations to the Moreau envelope -- and infimal convolutions more broadly -- based on Laplace's method, a classical tool in analysis which ties certain integrals to suprema of their integrands. We believe the connection…
We investigate strong maximum (and minimum) principles for fully nonlinear second order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of…
The alternating direction method of multipliers within a shape optimization framework is developed for solving geometric inverse problems, focusing on a cavity identification problem from the perspective of non-destructive testing and…
Shape optimization is commonly applied in engineering to optimize shapes with respect to an objective functional relying on PDE solutions. In this paper, we view shape optimization as optimization on Riemannian shape manifolds. We consider…
In this paper, we apply the framework of optimal transport to the formulation of optimal design problems. By considering the Wasserstein space as a set of design variables, we associate each probability measure with a shape configuration of…