4 citations · 6 across the 11 of their papers we have counts for
14 papers
EngramEdit: Decoupled Knowledge Updates in LLMs through Conditional Memory
Hongru Cai, Ran Wei, Wenjie Wang +4
Conditional memory architectures such as DeepSeek Engram use input n-grams to look up learned embeddings, expanding the capacity of large language models (LLMs) with limited additi…
Kobayashi visibility of strictly convex domains
Nikolai Nikolov, Amar Deep Sarkar
We show that any bounded strictly convex domain in , endowed with the Kobayashi distance, is visible.
A Canonical Positive Definite Kernel Associated with the -Bergman Kernel
Sahil Gehlawat, Aakanksha Jain, Amar Deep Sarkar
Let and . The -Bergman kernel , introduced by Bao and Guan, generalizes the classical Bergman kernel by replacing the point ev…
On the exponential convergence of Kobayashi geodesics in strongly convex domains
Kingshook Biswas, Sanjoy Chatterjee, Amar Deep Sarkar
In this paper, we have proved a quantitative version of the approaching geodesic property for certain convex domains. We have proved that that if is a bou…
Horofunction compactifications and local Gromov model domains
Vikramjeet Singh Chandel, Sushil Gorai, Anwoy Maitra +1
We explore the horofunction compactification of complete hyperbolic domains in complex Euclidean space equipped with the Kobayashi distance. We provide a sufficient condition under…
Visibility property in one and several variables and its applications
Vikramjeet Singh Chandel, Sushil Gorai, Anwoy Maitra +1
In this paper we report our investigations on visibility with respect to the Kobayashi distance and its applications, with a special focus on planar domains. We prove that totally…
A Note on Kernel Functions of Dirichlet Spaces
Sahil Gehlawat, Aakanksha Jain, Amar Deep Sarkar
For a planar domain , we consider the Dirichlet spaces with respect to a base point and the corresponding kernel functions. It is not known how these kernel functions be…
Localization of the Kobayashi distance for any visibility domain
Amar Deep Sarkar
In this article, we prove localization results for the Kobayashi distance of Kobayashi hyperbolic domains with local visibility property in , . This is done…
The Reduced Bergman Kernel and its Properties
Sahil Gehlawat, Aakanksha Jain, Amar Deep Sarkar
In this article, we study some properties of the -th order weighted reduced Bergman kernels for planar domains, . Specifically, we look at Ramadanov type theorems, loca…
Notions of Visibility with respect to the Kobayashi distance: Comparison and Applications
Vikramjeet Singh Chandel, Anwoy Maitra, Amar Deep Sarkar
In this article, we study notions of visibility with respect to the Kobayashi distance for relatively compact complex submanifolds in Euclidean spaces. We present a sufficient cond…
Transformation formula for the Reduced Bergman kernel and its Application
Sahil Gehlawat, Aakanksha Jain, Amar Deep Sarkar
In this article, we prove the transformation formula for the reduced Bergman kernels under proper holomorphic correspondences between bounded domains in the complex plane. As a cor…
Boundary behaviour of the Span metric and its higher-order curvatures
Amar Deep Sarkar
In this note, we use scaling principle to study the boundary behaviour of the span metric and its higher-order curvatures on finitely connected Jordan planar domains. A localizatio…
A submultiplicative property of the Carathéodory metric on planar domains
Amar Deep Sarkar, Kaushal Verma
Given a pair of smoothly bounded domains , the purpose of this note is to obtain an inequality that relates the Carathéodory metrics on $D_1, D_2, D_1 \…
Boundary behaviour of some conformal invariants on planar domains
Amar Deep Sarkar, Kaushal Verma
The purpose of this note is to use the scaling principle to study the boundary behaviour of some conformal invariants on planar domains. The focus is on the Aumann--Carathéodory ri…