Contact Form: Using SendGrid WebAPI and cURL PHP

Form.css

/* Form.html CSS, just copy and paste any where in your style.css file, or customize to fit with your domain */
form.contact p {
font-size: 15px;
padding: 0 0 15px 0;
margin: 0;
}

form.contact input, form.contact textarea {
font-family: Arial;
font-size: 15px;
margin: 0 0 20px 0;
}

form.contact textarea {
background: #f5f5f5;
padding: 5px;
border: 1px solid #bbb;
border-radius: 15px;
width: 400px;
height: 150px;
}

form.contact input {
background: #f5f5f5;
padding: 5px;
border: 1px solid #bbb;
border-radius: 15px;
}

form.contact input.send {
color: #fff;
background: #222;
border: #222;
padding: 10px 25px 10px 25px;
cursor: pointer;
}
/* End form.html's CSS */

Form.html

<!-- BEGINNING OF CONTACT FORM -->
<div class="section-page-landing" id="contact">
			<div class="inner-section">
				<div class="contain">
					<center><h2>Contact Me</h2>
<form class="contact" action="mailer.php" method="post">
<p>Name:</p> <!-- Can choose to customize form.html inputs starting here as needed, but be sure to reference any changes in mailer.php post fields-->
<input type="text" name="name" />
 <p>E-mail:</p>
<input type="text" name="email" />
<p>Subject:</p>
<input type="text" name="subject" />
<p>Message:</p>
<textarea name="message" syle="width: 45%; text-align: center;">Please leave a short message here</textarea></p>
<input class="send" type="submit" value="Send"> <!-- Send button-->
</form></center>
				</div>
			</div>
		</div>
		<!--end contact form-->

mailer.php

<?php

$curl = curl_init();
$name = $_POST['name']; 
$email = $_POST['email']; 
$subject = $_POST['subject']; 
$message = $_POST['message'];

curl_setopt_array($curl, array(
  CURLOPT_URL => "https://api.sendgrid.com/v3/mail/send",
  CURLOPT_RETURNTRANSFER => true,
  CURLOPT_ENCODING => "",
  CURLOPT_MAXREDIRS => 10,
  CURLOPT_TIMEOUT => 30,
  CURLOPT_HTTP_VERSION => CURL_HTTP_VERSION_1_1,
  CURLOPT_CUSTOMREQUEST => "POST",
  CURLOPT_POSTFIELDS => "{\n  \"personalizations\": [\n    {\n      \"to\": [\n        {\n          \"email\": \"[Email Address to send Contact to]\"\n        }\n      ],\n      \"subject\": \"New Contact\"\n    }\n  ],\n  \"from\": {\n    \"email\": \"[FROM EMAIL]\"\n  },\n  \"content\": [\n    {\n      \"type\": \"text/html\",\n      \"value\": \"$name<br>$email<br>$subject<br>$message\"\n    }\n  ]\n}",
  CURLOPT_HTTPHEADER => array(
    "authorization: Bearer [SG API key]",
    "cache-control: no-cache",
    "content-type: application/json"
  ),
));

$response = curl_exec($curl);
$err = curl_error($curl);

curl_close($curl);
header('Location: thanks.html');

if ($err) {
  echo "cURL Error #:" . $err;
} else {
  echo $response;
}

?>

Further investigation shows that the <br> tags are working as I have three blank lines in the email. The PHP variables are not coming through. I have tried adding things like <?= $message; ?> and other variants but that doesn't work.