Amsart Title Whitespace Problem

another method for countering the space above the title is to nullify the topskip
applied above the title. this is used elsewhere, so the value isn’t changed, but
a reversing vspace* is added after it:

usepackage{etoolbox}
makeatletter
patchcmd{@maketitle}{globaltopskip42[email protected]relax}
  {globaltopskip42[email protected]relax vspace*{-38pt}}
  {}{}
makeatother

it’s easy to change this value if you decide you want something slightly different.

the code should be put in your preamble. i suggest at the very top, immediately
following the documentclass line.

I don’t find the space is excessive. However, here’s an easy way for adjusting the spacing, act where indicated after experimenting with the values.

I removed your hack for sharing the counter between equations and theorems and alike environments to a better one.

Remove the showframe option to geometry for the production version.

documentclass[11pt,reqno]{amsart}

%-------Packages-----------------------
usepackage{amssymb,amsfonts}
usepackage[all,arc]{xy}
usepackage{enumerate}
usepackage{mathrsfs}
usepackage[a4paper, top=2.8cm, left=2cm, right=2cm, bottom=2cm,showframe]{geometry}
usepackage{wrapfig}
usepackage{tikz}
usepgflibrary{arrows} 
usepgflibrary[arrows] 
usetikzlibrary{arrows}
usetikzlibrary[arrows]
usetikzlibrary{automata} 
usetikzlibrary[automata] 
usetikzlibrary{positioning}
usepackage{framed}
usepackage{multicol}
usepackage{caption}
usepackage{subcaption}
usepackage{etoolbox}
usepackage{lipsum}      %used for this example
usepackage{hyperref}


%--------Theorem Environments----------
numberwithin{equation}{section}
newtheorem{thm}[equation]{Theorem}
newtheorem{cor}[equation]{Corollary}
newtheorem{prop}[equation]{Proposition}
newtheorem{lem}[equation]{Lemma}
newtheorem{conj}[equation]{Conjecture}
newtheorem{quest}[equation]{Question}

theoremstyle{definition}
newtheorem{defn}[equation]{Definition}
newtheorem{defns}[equation]{Definitions}
newtheorem{con}[equation]{Construction}
newtheorem{exmp}[equation]{Example}
newtheorem{exmps}[equation]{Examples}
newtheorem{notn}[equation]{Notation}
newtheorem{notns}[equation]{Notations}
newtheorem{addm}[equation]{Addendum}
newtheorem{exer}[equation]{Exercise}

theoremstyle{remark}
newtheorem{rem}[equation]{Remark}
newtheorem{rems}[equation]{Remarks}
newtheorem{warn}[equation]{Warning}
newtheorem{sch}[equation]{Scholium}

makeatletter
patchcmd{@settitle}
  {begin{center}}
  {vspace*{-3baselineskip}begin{center}}% <--- adjust the dimension
  {}{}
patchcmd{@setauthors}
  {30[email protected]}
  {20[email protected]}% <--- adjust the dimension
  {}{}
patchcmd{@setauthors}
  {endtrivlist}
  {endtrivlistvspace{-2baselineskip}}% <--- adjust the dimension
  {}{}
makeatother

bibliographystyle{plain}

%--------Info----------------------------
title{Title}
author{Author}
%----------------------------------------

begin{document}

maketitle

section{A title}

lipsum[1]

begin{thm}
A theorem statement with an equation
begin{equation}
x=x
end{equation}
and some text after it.
end{thm}

lipsum[2]

begin{rem}
A remark.
end{rem}

lipsum

end{document}

enter image description here

The vspace{-1cm} command inside author is of no use. Just type space*{-1.2cm}just before maketitle.

Alternatively you might want to take a look at the titling package, which provides tools to customise the maketitle command in a clean way.

Unrelated: the hyperref package should be loaded as the last one, with very few exceptions.

documentclass[11pt,reqno]{amsart}

 %-------Packages-----------------------
usepackage{amssymb,amsfonts}
usepackage[all,arc]{xy}
usepackage{enumerate}
usepackage{mathrsfs}
usepackage[a4paper, top=2.8cm, left=2cm, right=2cm, bottom=2cm, showframe]{geometry}
usepackage{wrapfig}
usepackage{tikz}
usepgflibrary{arrows}
usepgflibrary[arrows]
usetikzlibrary{arrows}
usetikzlibrary[arrows]
usetikzlibrary{automata}
usetikzlibrary[automata]
usetikzlibrary{positioning}
usepackage{framed}
usepackage{multicol}
usepackage{caption}
usepackage{subcaption}
usepackage[english]{babel} %used for this example
usepackage{blindtext} %used for this example
usepackage{hyperref}


%--------Theorem Environments----------
newtheorem{thm}{Theorem}[section]
newtheorem{cor}[thm]{Corollary}
newtheorem{prop}[thm]{Proposition}
newtheorem{lem}[thm]{Lemma}
newtheorem{conj}[thm]{Conjecture}
newtheorem{quest}[thm]{Question}

theoremstyle{definition}
newtheorem{defn}[thm]{Definition}
newtheorem{defns}[thm]{Definitions}
newtheorem{con}[thm]{Construction}
newtheorem{exmp}[thm]{Example}
newtheorem{exmps}[thm]{Examples}
newtheorem{notn}[thm]{Notation}
newtheorem{notns}[thm]{Notations}
newtheorem{addm}[thm]{Addendum}
newtheorem{exer}[thm]{Exercise}

theoremstyle{remark}
newtheorem{rem}[thm]{Remark}
newtheorem{rems}[thm]{Remarks}
newtheorem{warn}[thm]{Warning}
newtheorem{sch}[thm]{Scholium}

makeatletter
let[email protected][email protected]
makeatother
numberwithin{equation}{section}

bibliographystyle{plain}

%--------Info----------------------------
title{Title}
author{vspace{-0.5cm}Authorvspace{-1cm}}
%----------------------------------------

begin{document}

vspace*{-1.2cm}
maketitle
Blinddocument

end{document} 

enter image description here

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