16 citations · 65 across the 61 of their papers we have counts for
75 papers
The sharp constant in the Chang--Marshall inequality
Rupert L. Frank, Paata Ivanisvili
We prove that the optimal constant in the Chang--Marshall inequality is , as conjectured by Andreev and Matheson. More precisely, if is analytic in the unit disk, vanishes t…
Sharp comparison between the perimeter and its fractional analogue in two dimensions
Rupert L. Frank, Paata Ivanisvili
We show that the fractional perimeter of any order is maximal, among all planar sets of fixed perimeter, for the disk.
Polynomial growth of Bohnenblust--Hille constants on the Hamming cube
Paata Ivanisvili
We prove that the Bohnenblust--Hille constants for Walsh polynomials on the Hamming cube grow at most polynomially in the degree. More precisely, there is an absolute constant …
A proof of the Holmes-Holroyd-Ramirez cyclic-product conjecture
Paata Ivanisvili, Shengtong Zhang
We prove the cyclic-product conjecture of Holmes, Holroyd and Ramírez: among all circular arrangements of a decreasing positive sequence, the circular-symmetric ``greedy'' arrangem…
The Hayman--Wu constant is
Paata Ivanisvili
We show that for every conformal map from the unit disk onto a simply connected proper domain , the length of is at most…
A counterexample to the Kato conjecture for positive commutators
Rupert L. Frank, Paata Ivanisvili
We disprove the conjectural converse to Kato's positivity criterion for commutators of functions of the canonical position and momentum operators and by showing that the op…
Counterexamples to the Landis conjecture in dimensions three and higher
Rupert L. Frank, Paata Ivanisvili
In every dimension three and higher we construct a nonzero function that satisfies the stationary Schrödinger equation with bounded, real-valued potential and decays like $\exp(-c|…
The Winding Number at the Critical Hölder Exponent 1/3: Failure of Universal Fourier Summation
Rupert L. Frank, Paata Ivanisvili
The degree (or winding number) of a sufficiently regular map is given in terms of its Fourier coefficients by $$ \operatorname{deg} f = \sum_{n\in\…
The missing two-point inequality in Weissler's conjecture
Yi C. Huang, Paata Ivanisvili
Weissler's conjectured characterization of complex hypercontractivity on the Hamming cube remained open in the ranges and . Ivanisvili--Nazarov estab…
A Beckmann boundary form of Talagrand's conjecture on the discrete cube
Paata Ivanisvili, Xinyuan Xie, Haonan Zhang
We introduce the Beckmann boundary of a Boolean function \[ \mathsf{B}(f)=\inf_{\operatorname{div} V=Lf}\mathbb E\|V(x)\|_2. \] Here \[ L=\sum_iD_i,\qquad D_i f(x)=\frac{f(x)-f(x^{…
The distance between homotopy classes of Sobolev maps on spheres
Rupert L. Frank, Paata Ivanisvili
We consider self-maps of a sphere in the critical Sobolev space with a given Brouwer degree. Our main result is that the (directed) distance between maps of different degrees is eq…
Minimizers for Coulomb gases constrained to a halfspace
Rupert L. Frank, Paata Ivanisvili, Clara Torres-Latorre
We consider a family of optimization problems, based on a mean-field description of particles interacting through Coulomb forces in a quadratic trap. In addition, the particles are…
Geometric Block Exponents and a Uniform Mixed-Alphabet Sumset Inequality
Johannes Hosle, Paata Ivanisvili
We study sharp exponents in inequalities for pairs of finite geometric blocks. We characterize exactly when the endpoint determines the optimal exponent and compute the expon…
Dimension-free bounds for Riesz transforms on the Hamming cube via a Bellman function
Komla Domelevo, Paata Ivanisvili, Stefanie Petermichl +1
We give a Bellman-function proof of the dimension-free estimate \[ \Big\| \vec{R} f \Big\|_{L^p(Ω;\,\ell^2)} \lesssim (p-1) \,\|f\|_{L^p(Ω)}, \qquad 2\le p<\infty, \] for the vecto…
The sharp extension norm for a planar sector
Rupert L. Frank, Paata Ivanisvili
We compute explicitly the infimum of the norms of -extension operators for planar sectors and exhibit an extension operator attaining this infimum. This solves an open pro…
Carbery's inequality in the Schatten--von Neumann classes
Ziang Chen, Paata Ivanisvili, Jose Madrid +1
Carbery posed a question of sharpened triangle inequalities for families of operators in the Schatten--von Neumann classes , . He established a weaker form of the des…
The sharp log Sobolev inequality on finite cycles
Rupert L. Frank, Paata Ivanisvili
We settle the problem of finding the sharp constant in the log Sobolev inequality on the -cycle for all , by showing that it is equal to half of the spectral gap. We ded…
Grokability in five inequalities
Paata Ivanisvili, Xinyuan Xie
In this note, we report five mathematical discoveries made in collaboration with Grok, all of which have been subsequently verified by the authors. These include an improved lower…
Almost-Orthogonality in Lp Spaces: A Case Study with Grok
Ziang Chen, Jaume de Dios Pont, Paata Ivanisvili +2
Carbery proposed the following sharpened form of triangle inequality for many functions: for any and any finite sequence we have \[ \Big\|\sum_j f_j\B…
Sharp isoperimetric inequalities on the Hamming cube II: The critical exponent
Polona Durcik, Paata Ivanisvili, Joris Roos +1
A sharp isoperimetric inequality for the Hamming cube is proved at the critical exponent . This follows up on previous work, where such bounds were established for n…
Counterexample to majority optimality in NICD with erasures
Paata Ivanisvili, Xinyuan Xie
We asked GPT-5 Pro to look for counterexamples among a public list of open problems (the Simons ``Real Analysis in Computer Science'' collection). After several numerical experimen…
Optimal Young's convolutions inequality and its reverse form on the hypercube
David Beltran, Paata Ivanisvili, José Madrid +1
We establish sharp forms of Young's convolution inequality and its reverse on the discrete hypercube in the diagonal case . As applications, we derive bounds for a…
Multiversion of the Hausdorff--Young inequality
Paata Ivanisvili, Pavlos Kalantzopoulos
We consider a family of jointly Gaussian random vectors , each standard normal but possibly correlated, and investigate when\[ \mathbb{E}\, F\!\Bigl(B\big…
Sharp Lower Bounds for Dyadic Square Functions of indicator functions of sets
Natanael Alpay, Paata Ivanisvili
We study lower bounds for dyadic square functions of indicator functions. In the case of the dyadic square function we obtain a sharp lower bound: for every measurable $A \…